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In this paper, monocrystalline solar cell with different materials are analyzed and studied. Here, the solar cell is simulated for a single layer. The different materials used in our study are the semiconducting materials from group III-V semiconductors which are silicon (Si), Germanium (Ge), Indium Gallium Arsenide (InGaAs) and Indium Gallium Phosphide (InGaP). The monocrystalline solar cell simulation was done using PC1D software. The influence of different solar cell parameters, with their effects on efficiency, has been investigated. Parameters such as base thickness, emitter thickness, p-type and n-type doping concentrations are varied for different semiconductor materials. The chapter shows that the optimum magnitudes of base thickness and emitter thickness are $0.01 \mu \mathrm{m}$ and $1000 \mu \mathrm{m}$ respectively. And Indium Gallium Arsenide has the highest efficiency with a value of 19.37% for $1000 \mu \mathrm{m}$ base thickness and 34.31% for $0.01 \mu \mathrm{m}$ emitter thickness. It is also seen that the optimum value of n-type doping concentration is of the order $10^{17}/cm^{3}$ and p-type doping concentration is of the order $10^{17} /cm^{3}$ and with this optimum value, Indium Gallium Phosphide has the highest efficiency of 25.42% for p-type doping concentration and 22.18% for n-type doping concentration respectively. The effect of different antireflection coating (ARC) layers is also studied. It is shown that silicone nitrate is the best ARC layer with the maximum efficiency and in particular Indium Gallium Phosphide has the highest efficiency of 21.11%.

Energy stability theory is applied to the study of the nonlinear stability of natural convection in an inclined fluid layer having a uniform internal heat source (sink), with the boundaries of the layer maintained at constant temperatures. The stability limit is found in terms of the thermal Rayleigh number $$R_{1}$$ and the internal Rayleigh number $$R_{2}$$ . The region of stability is found in $$R_{1}$$ – $$R_{2}$$ plane where the base state is stable against arbitrary perturbations. The Prandtl number Pr of the fluid and the angle of inclination of the fluid layer play an important role in determining the stability region.

In non-monotonic reasoning, conditional belief bases mostly contain positive information in the form of standard conditionals. However, in practice we are often confronted with negative information, stating that a conditional does \emph{not} hold, i.e. we need a suitable approach for reasoning over belief bases $\Delta$ with positive and negative information. In this paper, we investigate the interaction of positive and negative information in a conditional belief base and establish a property for partitions of $\Delta$ that is equivalent to consistency. Based on this property, we develop a non-trivial extension of system Z for mixed conditional belief bases and provide an algorithm to compute this partition.

It has been more than 100 years since the advent of special relativity, but the reasons behind the related phenomena are still unknown. This article aims to inspire people to think about such problems. With the help of Mathematica software, I have proven the following problem by means of statistics: In 3-dimensional Euclidean space, for point particles whose speeds are c and whose directions are uniformly distributed in space (assuming these particles’ reference system is $$\mathcal {R}_{0}$$ R 0 , if their average velocity is 0), when some particles (assuming their reference system is $$\mathcal {R}_{u}$$ R u ), as a particle swarm, move in a certain direction with a group speed u (i.e., the norm of the average velocity) relative to $$\mathcal {R}_{0}$$ R 0 , their (or the sub-particle swarm’s) average speed relative to $$\mathcal {R}_{u}$$ R u is slower than that of particles (or the same scale sub-particle swarm) in $$\mathcal {R}_{0}$$ R 0 relative to $$\mathcal {R}_{0}$$ R 0 . The degree of slowing depends on the speed u of $$\mathcal {R}_{u}$$ R u and accords with the quantitative relationship described by the Lorentz factor $$\frac{c}{\sqrt{c^2-u^2}}$$ c c 2 - u 2 . Base on this conclusion, I have deduced the speed distribution of particles in $$\mathcal {R}_{u}$$ R u when observing from $$\mathcal {R}_{0}$$ R 0 .

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generaliza- tion of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from LΨ. As a measure of such approximation we will use the function constructed by function Ψ com- plementary to Φ on the base of definition of the LΨ points. Some corollary and remarks will also be given.

This brief presents a high precision high-order curvature-compensated bandgap voltage reference (BGR) with a 3.11-V output voltage for battery-management integrated circuits. The proposed circuit utilizes the exponential characteristics of the base current and the resistance between bases of bipolar transistors to perform corrections. The curvature of subthreshold-operating MOSFETs is considered to further compensate for high-order temperature effects over a wide temperature range of 170 °C. Test results for the proposed BGR fabricated utilizing a standard 0.18- ${\mu }\text{m}$ BiCMOS process demonstrate that its line regulation is approximately 0.31 mV/V in a supply voltage range of 4.2–6.0 V. with 4-bit trimming, a temperature coefficient of 4.6 ppm/°C is obtained in the range of −40 °C to 130 °C. The active area of the proposed BGR is 634 ${\times }$ 351 ${\mu }\text{m}$ .

The Σ -protocols for homomorphism relations are one of the cryptographic protocols which are used to prove knowledge of homomorphism relations. The Schnorr protocol is one of the most famous Σ -protocols used for proving knowledge of discrete logarithm (DL) relation in which the verifier essentially performs one double-exponentiation (i.e. a group computation of the form axby ). A direct application of the Schnorr protocol for proving simultaneous knowledge of n DLs with a common base leads to a Σ -protocol in which the verifier performs n double-exponentiations. In this study, the authors propose another Σ -protocol for homomorphism relations. The proposed Σ -protocol has fast verification when is used to prove the simultaneous homomorphism relations with a common homomorphism. Also, when the DL instantiation (DL-instantiation) of the proposed Σ -protocol is used to prove simultaneous knowledge of n DLs with a common base, it leads to a Σ -protocol in which the verifier performs n+1 single-exponentiations.

The impact of scaling of the base layer on the noise performance, spectral responsivity, and frequency response of Ge/Ge1– x Sn x /Ge p-n-p heterojunction phototransistor (HPT) is presented and evaluated by simulation. The proposed structure consists of Ge1– x Sn x alloy in the base layer, allowing extension of the photodetection to the mid-infrared (MIR) region, enabling photodetection over a wide range. This paper also includes the effect of Sn concentration and base bias voltage on the frequency performance of the HPT. In addition, various noise components and signal-to-noise ratio (SNR) are estimated as a function of base layer thickness and base resistance. The simulated results show that cutoff frequency ( ${f}_{T}$ ) and maximum frequency ( ${f}_{\text {max}}$ ) are not only strongly dependent on the base layer thickness but also on the Sn composition in the base layer and applied base-bias voltage. The results show that the proposed HPT provides higher ${f}_{T} >45$ GHz and SNR of >70 dB for the base layer thickness of 50 nm (with Sn = 9%) can be achieved. Therefore, the GeSn p-n-p HPT is promising for future fiber-optic telecommunication and MIR applications.

The Thue-Morse set T is the set of those non-negative integers whose binary expansions have an even number of 1. The name of this set comes from the fact that its characteristic sequence is given by the famous Thue-Morse word abbabaabbaababba..., which is the fixed point starting with a of the word morphism sending a to ab and b to ba. The numbers in T are sometimes called the evil numbers. We obtain an exact formula for the state complexity (i.e. the number of states of its minimal automaton) of the multiplication by a constant of the Thue-Morse set with respect to any integer base b which is a power of 2. Our proof is constructive and we are able to explicitly provide the minimal automaton of the language of all 2^p-expansions of the set mT for any positive integers m and p. The used method is general for any b-recognizable set of integers. As an application, we obtain a decision procedure running in quadratic time for the problem of deciding whether a given 2^p-recognizable set is equal to some multiple of the Thue-Morse set., In Proceedings GandALF 2019, arXiv:1909.05979. Short paper. A full version of this paper appears as arXiv:1903.06114

We prove results concerning rational function solutions of the functional equations arising from multiplication of quantum integers and thus resolve some problems raised by Melvyn Nathanson. First, we show that the rational function solutions contain more structure than the polynomial solutions in an essential way, namely the non-cyclotomic part of the former is no longer necessarily trivial, which allows us to resolve a problem on the associated Grothendieck group \(K(\Upsilon _{P})\) of the collection of all polynomial solutions \(\Upsilon _{P}\) with fields of coefficients of characteristic zero and support base P. Second, we show that, contrary to the polynomial solution case, there exists at least one (infinitely many) rational function solution, with support base P containing all primes, which are not constructible from quantum integers. Third, we show that even in the case where the non-cyclotomic part is trivial, rational function solutions are different from polynomial solutions in that there still exist infinitely many rational function solutions to these functional equations with support base P containing all primes and which are not constructible from quantum integers.

Let us be given a rooted digraph D = ( V + s , A ) with a designated root vertex s . Edmonds' seminal result [Edmonds, J., Edge-disjoint branchings , in: B. Rustin (ed.) Combinatorial Algorithms, Academic Press, New York, 91–96 (1973] states that D has a packing of k spanning s -arborescences if and only if D has a packing of k ( s , t )-paths for all t ∈ V , where a packing means arc-disjoint subgraphs. Let M be a matroid on the set of arcs leaving s . A packing of ( s , t )-paths is called M -based if their arcs leaving s form a base of M while a packing of s -arborescences is called M -based if, for all t ∈ V , the packing of ( s , t )-paths provided by the arborescences is M -based. Durand de Gevigney, Nguyen and Szigeti proved in [Durand de Gevigney, O., V.H. Nguyen, and Z. Szigeti, Matroid-based packing of arborescences , SIAM J. Discrete Math., 27 (2013), 567–574] that D has an M -based packing of s -arborescences if and only if D has an M -based packing of ( s , t )-paths for all t ∈ V . Berczi and Frank conjectured that this statement can be strengthened in the sense of Edmonds' theorem such that each s -arborescence is required to be spanning. Specifically, they conjectured that D has an M -based packing of spanning s -arborescences if and only if D has an M -based packing of ( s , t )-paths for all t ∈ V . We disprove this conjecture in its general form and we prove that the corresponding decision problem is NP-complete. However, we prove that the conjecture holds for several fundamental classes of matroids, such as graphic matroids and transversal matroids.

We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for $$\varDelta _0$$ formulae are provable in $$\mathbf {I}\varvec{\Sigma }_n$$. It is shown to be larger than the proof-theoretic ordinal $$|\mathbf {I}\varvec{\Sigma }_n|$$ by power of base 2. We also show a similar result for the structural transfinite induction, defined with fundamental sequences.

Recently, it is found that the bit error rate performance can be improved by optimizing the edge connections between the source code and the channel code ( ${B}_{L1}$ or ${B}_{L2}$ in the joint base matrix ${B}_{J}$ ) for joint source-channel coding system based on double protograph low density parity check codes. In this letter, the connection relationship in ${B}_{L1}$ from the angle of both the source code and the channel code is analyzed, where the protograph LDPC codes with various row weights used as the source code are taken into account. And a search algorithm for ${B}_{L1}$ under the constraints is proposed based on the joint protograph extrinsic information transfer (JPEXIT) and the source PEXIT to improve the performance. Both the JPEXIT analysis and the simulation results indicate that the performance of the searched optimal scheme has considerable gain compared with the conventional solutions.

Let G = (V (G), E(G)) be any undirected graph. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G[A] = V (G)\N_G[A], where N_G[A] = A ∪ { x : xa ∈ E(G) for some a ∈ A } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the corona, edge corona, disjunction, symmetric difference, Tensor product, and the strong product of two graphs by determining the subbasic open sets.

Quantitative relationships between the active acidity $${\text{(p}}{{{\text{H}}}_{{{{{\text{H}}}_{2}}{\text{O}}}}})$$ of peat soils on the one hand and their exchange acidity (pHKCl), nonexchangeble (total potential) acidity (1M CH3COONa extract), contents of exchange cations and alkaline-earth bases, and base saturation degree, on the other hand, have been identified in the form of a linear function. Coefficients of the resultant regression equations are provided. The high predictive capability of the produced regression models is proven using independent data as examples. The use of regression equations eliminates the need for time-consuming chemical analytical works, thus making it possible to operatively classify wetlands and peat soils on the basis on their chemical properties: saturation with alkaline-earth bases and pH value. The botanical composition may also be used as a reliable indicator, provided that the degree of peat decomposition is low and subject to special knowledge of morphology and anatomy of sphagnum mosses and vascular swamp plants.

We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a modular interpretation for these schemes and compute them explicitly in a number of standard families. For two such families the computation is based on a symmetric version of homological projective duality for $\mathbb{P}^2 \times \mathbb{P}^2$ and $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, which we explain in an appendix., Comment: 48 pages; v2: minor improvements

The purpose of this paper is the study of intuitionistic fuzzy subhypergroups of some special finite complete hypergroups. More exactly, in this paper we determine all m-tuples, characterizing the considered complete hypergroups, such that the grade intuitionistic fuzzy set $$(\overline{\mu },\overline{\lambda })$$ is an intuitionistic fuzzy subhypergroup of such hypergroups. Here, we deal with complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo $$p^2$$ or modulo pq, with p and q distinct odd primes. This article is a continuation of a previous work, concerning the complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo p or modulo 2p, with p a prime number. It represents the starting point, the mathematical base, for writing a general algorithm for characterizing all complete hypergroups obtained from a group G and having the grade intuitionistic fuzzy set as an intuitionistic fuzzy subhypergroup.

The study assesses the proximate composition, amino acid profile and its content and chemical indices of the sun-dried Schilbe mystus, Bagrus bayad, Oreochromis niloticus, Clarias anguillaris and Petrocephalus bane bane from Tiga Dam Reservoir, Nigeria. The proximate composition varied significantly (pP. bane bane was first in terms of crude protein; S. mystus had the highest lipid and essential amino acid content. Also, C. anguillaris recorded the highest calorific value and best amino acid content. Thus, P. bane bane can serve as a source of animal protein to balance deficiencies in humans. Both S. mystus and C. anguillaris can be used as a nutrient base for high energy food and oil in the food industry.

The new concept of antineutrino source for future short-baseline experiments is discussed. The source ensures: 1) well defined hard antineutrino flux; 2) the rate of counts more than ~(1E+2 - 1E+3) per day in the detector volume about cubic meter; 3) low level of count errors - < 1%. The proposed source is based on (n,gamma)-activation of 7Li near the reactor active zone and transport of the fast beta-decaying 8Li isotope toward a remote neutrino detector and back in the closed loop. The proposed experiment allows to detect (electron antineutrino, p)-interaction with high precision and directed to search of sterile neutrinos with squared-mass difference between sterile and active neutrinos ~1 eV2. The results of simulation for (3+1) and (3+2) sterile neutrino models indicate the space regions for search of electron antineutrino-disappearance outside the spectrum errors., 14 pages; 9 figures; 34 references

2,6-Dichlorohydroquinone 1,2-dioxygenase (PcpA) is a non-heme Fe(II) enzyme that is specific for ortho-dihalohydroquinones. Here we deconvolute the role of halogen polarizability vs. substrate pKa in defining this specificity, and show how substrate binding compares to the structurally homologous catechol extradiol dioxygenases. The substrates 2,6-dichloro- and 2,6-dibromohydroquinone (polarizable halogens, pKa1 = 7.3), 2,6-difluorohydroquinone (nonpolarizable halogens, pKa1 = 7.5), and 2-chloro-6-methylhydroquinone (polarizable halogen, pKa1 = 9.0) were examined through spectrophotometric titrations and steady-state kinetics. The results show that binding of the substrates to the enzyme decreased $$pK_{a1}^{\text{app}}$$ by about 0.5, except for 2,6-difluorohydroquinone, which showed no change. Additionally, the Kd values of 2,6-dichloro- and 2,6-dibromohydroquinone are about equal to their respective $$K_{\text{mA}}^{\text{app}}$$ . For comparison, with catechol 2,3-dioxygenase (XylE), the substrates 4-methyl- and 3-bromocatechol are bound to the enzyme exclusively in the monoanion form over a wide pH range, indicating a $$\Delta pK_{a1}^{\text{app}}$$ of at least − 2.9 and − 1.2, respectively. The steady-state kinetic studies showed that 2,6-difluorohydroquinone is a poor substrate, with $${{k_{\text{cat}}^{\text{app}} } \mathord{\left/ {\vphantom {{k_{\text{cat}}^{\text{app}} } {K_{\text{mA}}^{\text{app}} }}} \right. \kern-0pt} {K_{\text{mA}}^{\text{app}} }}$$ approximately 40-fold lower and $$K_{\text{mA}}^{\text{app}}$$ 20-fold higher than 2,6-dichlorohydroquinone, despite its similar pKa1. Likewise, the pH dependence of $$k_{\text{cat}}^{\text{app}}$$ for 2-chloro-6-methylhydroquinone is nearly identical to that of 2,6-dichlorohydroquinone, despite its very different pKa1. These results show that (1) it is clearly the halogen polarizability and not the lower substrate pKa that determines the substrate specificity of PcpA, and (2) that PcpA, unlike the catechol extradiol dioxygenases, lacks an active site base that assists with substrate deprotonation, highlighting a key functional difference in what are otherwise similar active sites that defines their different reactivity.

The ground deicing heating system is an important equipment to ensure flight safety of civil aircraft in winter. As the main element, the heating tube directly affects the working efficiency of the system. The deicing fluid is high viscosity mixture. To improve heating efficiency of deicing fluid, a new special-shaped tube is proposed, which is named double-spiral trapezoidal grooved tube. The upper base width (m), groove depth (h) and base angle (θ) are the important structural parameters of the new tube. The optimal Latin hypercube design is applied to carry out the experiment design of m, h and θ. Nusselt number (Nu), flow resistance coefficient (f) and performance evaluation criteria (PEC) are selected as the optimization objectives. Then, the response surface approximation model is established to conduct sensitivity analysis. Based on the model, NCGA and NSGA-II algorithms are, respectively, introduced to perform the multi-objective optimization. The results show that NSGA-II is better than NCGA. When $$m \in \left[ {0.17, \, 0.33} \right]$$ , $$h \in [1.06, \, 1.08]$$ and $$\theta \in \left[ {84.06, \, 84.75} \right]$$ , the best range of optimization objectives is $$Nu \in \left[ {86.04, \, 87.81} \right]$$ , $$f \in \left[ {0.70, \, 0.73} \right]$$ and $${\text{PEC}} \in \left[ {1.60, \, 1.62} \right]$$ . With the growth of turbulence intensity, PEC > 1, and Nu increases by 4–27%. As a result, the heating efficiency of the new tube is superior to the original tube.

In this study we introduce a new series space | Fθ| (p) as the domain of a matrix corresponding to the absolute Fibonacci summability in the Maddox’s space l(p) and show that it is linearly isomorphic to the space l(p) and that it is an FK-space. Also, we determine its duals, base and characterize certain matrix transformations on that space. © 2019, Unione Matematica Italiana.

Let C be the Cantor set. For each n ⩾ 3 we construct an embedding A : C × C → R n such that A ( C × { s } ) , for s ∈ C , are pairwise ambiently incomparable everywhere wild Cantor sets (generalized Antoine's necklaces). This serves as a base for another new result proved in this paper: for each n ⩾ 3 and any non-empty perfect compact set X which is embeddable in R n − 1 , we describe an embedding A : X × C → R n such that each A ( X × { s } ) , s ∈ C , contains the corresponding A ( C × { s } ) , and is “nice” on the complement A ( X × { s } ) − A ( C × { s } ) ; in particular, the images A ( X × { s } ) , for s ∈ C , are ambiently incomparable pairwise disjoint copies of X. This generalizes and strengthens theorems of J.R. Stallings (1960), R.B. Sher (1968), and B.L. Brechner–J.C. Mayer (1988).

Predictions from embedded-LES are presented of a model of a section of a double-stacked freight wagon subjected to different local loading configurations. In total, 15 different upstream ( G f r o n t ) and downstream ( G b a s e ) gap spacings were simulated to characterise the change in the flow topology. The mean flow fields indicate that the inter-wagon flow undergoes a significant topology change over the range of G f r o n t = 1.77 W – 3.23 W ( W = wagon width). For G f r o n t ≤ 1.77 W , the mean recirculating flow in the gap covers its entire length. In contrast, for G f r o n t ≳ 3.23 W , the complete wake closure for the upstream wagon occurs enabling the upstream shear layers to impinge on the entire downstream surface, in turn, increasing the rate of change of drag force as G f r o n t is increased. The change in the wake shedding frequency, directly affecting the base pressure and consequently the drag, due to the variation in G f r o n t and G b a s e , is presented.

Let $\mathbf{M}$ be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, $\Delta_0$-separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set-theoretic collection scheme to $\mathbf{M}$. We focus on two common parameterisations of collection: $\Pi_n$-collection, which is the usual collection scheme restricted to $\Pi_n$-formulae, and strong $\Pi_n$-collection, which is equivalent to $\Pi_n$-collection plus $\Sigma_{n+1}$-separation. The main result of this paper shows that for all $n \geq 1$, (1) $\mathbf{M}+\Pi_{n+1}\textrm{-collection}+\Sigma_{n+2}\textrm{-induction on } \omega$ proves the consistency of Zermelo Set Theory plus $\Pi_{n}$-collection, (2) the theory $\mathbf{M}+\Pi_{n+1}\textrm{-collection}$ is $\Pi_{n+3}$-conservative over the theory $\mathbf{M}+\textrm{strong }\Pi_n \textrm{-collection}$. It is also shown that (2) holds for $n=0$ when the Axiom of Choice is included in the base theory. The final section indicates how the proofs of (1) and (2) can be modified to obtain analogues of these results for theories obtained by adding fragments of collection to a base theory (Kripke-Platek Set Theory with Infinity and $V=L$) that does not include the powerset axiom., Comment: 22 pages

The Stewart-Figge acid–base model has been criticized for being mathematically complex. We aimed to develop simpler formalisms, which can be used at the bedside. The following simplifications were used: (1) [Ca2+] and [Mg2+] are replaced by their mid-reference concentrations (2) pH is set to 7.4. In the new model [SIDa] is replaced by its adjusted form, [SIDa, adj] = [Na+] + [K+] − [Cl−] + 6.5 and [SIG] is replaced by “bicarbonate gap”, [BICgap] = [SIDa, adj] − (0.28⋅[Albumin]) − (1.82⋅[Phosphatei])- [HCO3]. The diagnostic performance of the model was tested in 210 patients with acute respiratory diseases and 17 healthy volunteers. [BICgap] was also compared to albumin-corrected anion gap ([AGc]). The concordant correlation coefficient between [SIDa, adj] and [SIDa] and between [BICgap] and [SIG] was 0.98 in both comparisons. The mean bias (limits of agreement) of [SIDa, adj] − [SIDa] and of [BICgap] − [SIG] were 0.53 meq/l (− 0.46 to 1.53) and 0.50 meq/l (− 0.70 to 1.70), respectively. A [SIDa, adj] 52.5 meq/l had an accuracy of 0.997 (p 11.6 meq/l predicted unmeasured ion (UI) acidosis with an accuracy of 0.997 (p 19.88 meq/l predicted UI acidosis with an accuracy of 0.994 (p

A protein is commonly visualized as a discrete piecewise linear curve, conventionally characterized in terms of the extrinsically determined Ramachandran angles. However, in addition to the extrinsic geometry, the protein has also two independent intrinsic geometric structures, determined by the peptide planes and the side chains respectively. Here we develop a novel 3D visualization method that instead of the extrinsic geometry utilizes the intrinsic geometry of side chains. We base our approach on a series of orthonormal coordinate frames along the protein side chains in combination with a mapping of the atoms positions onto a unit sphere, for visualization purposes. We develop our methodology in terms of an example, by analyzing the acidity dependence of the presumed myoglobin ligand gate. In the literature, the ligand gate is often asserted to be highly localized at the distal histidine, its functioning being regulated by environmental changes. Thus, we investigate whether any $${\mathrm{pH}}$$ dependence can be detected in the orientation of the distal and proximal histidine residues, using existing crystallographic data. We observe no $${\mathrm{pH}}$$ dependence, in support of the alternative proposals that the ligand gate is more complex and might even be located elsewhere. Our methodology should help the planning of future myoglobin structure experiments, to identify the ligand gate position and its mechanism. More generally, our methodology is designed to visually depict the spatial orientation of side chain covalent bonds in a protein. As such, it can be eventually advanced into a general visual 3D tool for protein structure analysis for purposes of prediction, validation and refinement. It can serve as a complement to widely used visualization suites such as VMD, Jmol, PyMOL and others.

Given a positive integer M, let B ℵ 0 ( M ) be the set of bases q > 1 such that there exists a real number x with exactly ℵ 0 different q-expansions over the alphabet { 0 , 1 , … , M } . It is known that the smallest base in B ℵ 0 ( M ) is G ( M ) , the generalized golden ratio. In this paper we investigate the next smallest element q ℵ 0 ( M ) of B ℵ 0 ( M ) , and show that if M = 2 m , q ℵ 0 ( M ) is the appropriate root of q 3 = m q 2 + ( m + 1 ) q + 1 , and if M = 2 m − 1 , q ℵ 0 ( M ) is the appropriate root of q 6 = ( m − 1 ) q 5 + ( 2 m − 1 ) q 4 + ( 2 m − 1 ) q 3 + 2 m q 2 + m q + 1 .

We investigate different concepts related to D-spaces. We show that any space with an ω 0 -Noetherian point network is hereditarily thickly covered. To distinguish monotonically monolithic spaces and spaces with predictable network, we show that there exists a monotonically monolithic space which doesn't have a predictable network under the assumption 2 ω 0 2 ω 1 . This provides a consistent negative answer to one of Guo and Junnila's questions in [16] . Some sufficient conditions for a strongly monotonically monolithic space to have a point-countable base are also given.

We consider the problem of integration of L_\infty-algebroids (differential graded manifolds) to L_\infty-groupoids. We first construct a "big" Kan simplicial manifold (Fr\'echet or Banach) whose points are solutions of a (generalized) Maurer-Cartan equation. The main analytic trick in our work is an integral transformation sending the solutions of the Maurer-Cartan equation to closed differential forms. Following ideas of Ezra Getzler we then impose a gauge condition which cuts out a finite-dimensional simplicial submanifold. This "smaller" simplicial manifold is (the nerve of) a local Lie k-groupoid. The gauge condition can be imposed only locally in the base of the L_\infty-algebroid; the resulting local k-groupoids glue up to a coherent homotopy, i.e. we get a homotopy coherent diagram from the nerve of a good cover of the base to the (simplicial) category of local Lie k-groupoids. Finally we show that a m-symplectic differential graded manifold integrates to a local m-symplectic Lie k-groupoid; globally these assemble to form an A_\infty-functor. As a particular case for m=2 we obtain integration of Courant algebroids., Comment: 26 pp; v4: minor changes (the published version)

Given a real number $$ \beta > 1$$ , we study the associated $$ (-\,\beta )$$ -shift introduced by Ito and Sadahiro. We compare some aspects of the $$(-\,\beta )$$ -shift to the $$\beta $$ -shift. When the expansion in base $$ -\,\beta $$ of $$ -\,\frac{\beta }{\beta +1} $$ is periodic with odd period or when $$ \beta $$ is less than the golden ratio, the $$ (-\,\beta )$$ -shift cannot be coded because its language is not transitive. This intransitivity of words explains the existence of gaps in the interval $$[-\,\frac{\beta }{\beta +1}, \frac{1}{\beta +1})$$ . We observe that an intransitive word appears in the $$(-\,\beta )$$ -expansion of a real number taken in the gap. Furthermore, we determine the Zeta function $$\zeta _{-\,\beta }$$ of the $$(-\,\beta )$$ -transformation and the associated lap-counting function $$L_{T_{-\,\beta }}$$ . These two functions are related by $$\zeta _{-\,\beta }=(1-z^2)L_{T_{-\,\beta }}$$ . We observe some similarities with the zeta function of the $$\beta $$ -transformation. The function $$\zeta _{-\,\beta }$$ has a simple pole at $$ \frac{1}{\beta }$$ and no other singularities z such that $$\vert z \vert =\frac{1}{\beta }$$ . We also note an influence of gaps ( $$\beta $$ less than the golden ratio) on the zeta function.

The natural exponential potential ( $$C\hbox {e}^{-R/{\lambda _0 }})$$ widely exists at micro/nanoscales; this paper studies the interaction potential between a curved-surface body and an outside particle base on the natural exponential potential. Mathematical derivation proves that the interaction potential can be expressed as a function of curvatures. Then, idealized numerical experiments are designed to verify the accuracy of the curvature-based potential. The driving forces exerted on the particle are discussed and confirmed to be a function of curvatures and the gradient of curvatures, which may explain some abnormal movements at micro/nanoscales.

This review gives some information about imidazole ring as a ( ligand , complex , antimicrobial , antimalarial , anticancer , uses , applications , linked with active groups such as Schiff base , azo group , ..).

The crystal-chemical structure, band gap-grain structure and dielectric properties of (1−x)SrTiO3-xCe0.95Zr0.05O2 [(Sr,Ce,Zr)TiO3, for x = 0.0, 0.3 and 0.4] ceramics were investigated. Samples with 0.3 ≤ x ≤ 0.4 appeared cubic by X-ray diffraction (XRD), however, splitting of the peaks along with Rietveld refinement indicated tetragonal structure. The change in the band gap energy with Ce(x) have been investigated and are related to variation in the grain size, activation energy and octahedral tilting. The reduction in band gap energy with Ce0.95Zr0.05O2 ions (x = 0.4) is attributed to the widening of conduction band with octahedral tilting. The absence of TO2 (175 cm−1) mode while the existence of TO4 (521.72 cm−1) mode has been considered as sign of relaxor-like-dielectric behavior. The e′−T curve and the P–E loop analysis confirms that there is no signature of the ferroelectric phase in all samples. Base on the X-ray photoelectrons spectroscopy (XPS) and high temperature ac conductivity analysis, the dielectric anomalies were due to the formation of lattice defects and defect dipoles ( $$~{\text{T}}{{\text{i}}^{{\text{4}}+}} \bullet \text{e}^{\prime} - V_{o}^{{ \bullet \bullet }} - {\text{T}}{{\text{i}}^{{\text{4}}+}} \bullet \text{e}^{\prime}~$$ , and $${V^{\prime\prime}_{Sr}} - ~V_{o}^{{ \bullet \bullet }}$$ ) generated by the Ti3+ ions and ionized oxygen vacancies.

The Golomb space $\mathbb N_\tau$ is the set $\mathbb N$ of positive integers endowed with the topology $\tau$ generated by the base consisting of arithmetic progressions $\{a+bn\}_{n=0}^\infty$ with coprime $a,b$. We prove that the Golomb space $\mathbb N_\tau$ has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set $\Pi$ of prime numbers is a dense metrizable subspace of $\mathbb N_\tau$, and each homeomorphism $h$ of $\mathbb N_\tau$ has the following properties: $h(1)=1$, $h(\Pi)=\Pi$ and $\Pi_{h(x)}=h(\Pi_x)$ for all $x\in\mathbb N$. Here by $\Pi_x$ we denote the set of prime divisors of $x$., Comment: 12 pages

There are two standard approaches to the construction of \begin{document}$ t $\end{document} -designs. The first one is based on permutation group actions on certain base blocks. The second one is based on coding theory. The objective of this paper is to give a spectral characterisation of all \begin{document}$ t $\end{document} -designs by introducing a characteristic Boolean function of a \begin{document}$ t $\end{document} -design. The spectra of the characteristic functions of \begin{document}$ (n-2)/2 $\end{document} - \begin{document}$ (n, n/2, 1) $\end{document} Steiner systems are determined and properties of such designs are proved. Delsarte's characterisations of orthogonal arrays and \begin{document}$ t $\end{document} -designs, which are two special cases of Delsarte's characterisation of \begin{document}$ T $\end{document} -designs in association schemes, are slightly extended into two spectral characterisations. Another characterisation of \begin{document}$ t $\end{document} -designs by Delsarte and Seidel is also extended into a spectral one. These spectral characterisations are then compared with the new spectral characterisation of this paper.

Kahan discretization is applicable to any quadratic vector field and produces a birational map which approximates the shift along the phase flow. For a planar quadratic Hamiltonian vector field with a linear Poisson tensor and with a quadratic Hamilton function, this map is known to be integrable and to preserve a pencil of conics. In the paper "Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation" by P. van der Kamp et al. [ 5 ], it was shown that the Kahan discretization can be represented as a composition of two involutions on the pencil of conics. In the present note, which can be considered as a comment to that paper, we show that this result can be reversed. For a linear form \begin{document}$ \ell(x,y) $\end{document} , let \begin{document}$ B_1,B_2 $\end{document} be any two distinct points on the line \begin{document}$ \ell(x,y) = -c $\end{document} , and let \begin{document}$ B_3,B_4 $\end{document} be any two distinct points on the line \begin{document}$ \ell(x,y) = c $\end{document} . Set \begin{document}$ B_0 = \tfrac{1}{2}(B_1+B_3) $\end{document} and \begin{document}$ B_5 = \tfrac{1}{2}(B_2+B_4) $\end{document} ; these points lie on the line \begin{document}$ \ell(x,y) = 0 $\end{document} . Finally, let \begin{document}$ B_\infty $\end{document} be the point at infinity on this line. Let \begin{document}$ \mathfrak E $\end{document} be the pencil of conics with the base points \begin{document}$ B_1,B_2,B_3,B_4 $\end{document} . Then the composition of the \begin{document}$ B_\infty $\end{document} -switch and of the \begin{document}$ B_0 $\end{document} -switch on the pencil \begin{document}$ \mathfrak E $\end{document} is the Kahan discretization of a Hamiltonian vector field \begin{document}$ f = \ell(x,y)\begin{pmatrix}\partial H/\partial y \\ -\partial H/\partial x \end{pmatrix} $\end{document} with a quadratic Hamilton function \begin{document}$ H(x,y) $\end{document} . This birational map \begin{document}$ \Phi_f:\mathbb C P^2\dashrightarrow\mathbb C P^2 $\end{document} has three singular points \begin{document}$ B_0,B_2,B_4 $\end{document} , while the inverse map \begin{document}$ \Phi_f^{-1} $\end{document} has three singular points \begin{document}$ B_1,B_3,B_5 $\end{document} .

The second approximation of the theory of narrow ribbon beams with a curvilinear axis and plane-symmetric flows is formulated. A complete hydrodynamic picture of the flow near the starting surface upon the emission in the $$\rho $$ - and T-modes is constructed. The neighborhood of the singular points corresponding to the extrema of the potential at the base tube of current during its nonmonotonic change is studied.

A novel ultrafast and low-loss lateral injection-enhanced gate transistor (LIEGT) is proposed and investigated by simulation. The device features a MOS-controlled shorted anode (MCSA) and a bias voltage ( ${V}_{{AG}}$ ) applied between the anode trench gate (ATG) and the anode electrode. The n+ anode is shorted to the N-buffer through the MOS channel around the ATG when the MCSA is activated with ${V}_{{AG}} > {V}_{{th}}$ during turn-off and blocking states, and thus the p+ anode/N-buffer junction is unactivated. The MCSA LIEGT turns off as fast as a unipolar device by optimizing the time gap to activate the MCSA before turning off the cathode trench gate (CTG). The activated MCSA would deactivate hole injection from the anode side and synchronously quickly extract the electrons from the N-drift, which improves the switching speed and dramatically decreases the turn-off energy loss ( ${E}_{ \mathrm{\scriptscriptstyle OFF}}$ ). In the blocking state, the MCSA LIEGT achieves a MOS breakdown mode instead of an open base p-n-p bipolar breakdown mode. Thus, the breakdown voltage (BV) is not only improved but also independent of the p+ anode doping concentration. In the forward conduction state with ${V}_{{AG}} = {0}$ , the MCSA is unactivated and hence the MCSA LIEGT operates like a conventional LIEGT without deteriorating the on-state voltage drop ( ${V}_{ \mathrm{\scriptscriptstyle ON}}$ ). Compared with the conventional LIEGT, the proposed device decreases ${E}_{ \mathrm{\scriptscriptstyle OFF}}$ by 88% and improves the BV by 13% at the same ${V}_{ \mathrm{\scriptscriptstyle ON}}$ . Importantly, ${E}_{ \mathrm{\scriptscriptstyle OFF}}$ is almost independent of ${V}_{ \mathrm{\scriptscriptstyle ON}}$ .

In this paper, we investigate a vertical gate-based elevated tunnel source (TS) FET structure with and without a vertical n+ pocket and compare its performance with a lateral p-n-i-n TS (LTS) FET. The lined arrangement of gate not only provides a performance boosting as expected but it further allows the flexibility to minimize the degradations at higher pocket doping using source elevation. The vertical gate and pocket alignment overcome the full-depletion constraint of the LTS FET and maintain a better subthreshold swing (SS) over a higher range of pocket doping and width. An optimized average SS as low as ~26 mV/dec is achieved over five decades of current which is improved by 58% and 67%, respectively, as compared to the LTS and p-i-n tunnel field-effect transistors (TFETs) with an on-current enhancement of one order and $\sim 17\times $ , respectively. Furthermore, the gate-to-drain capacitance ( ${C} _{\textsf {GD}}$ ) in elevated source structures is a highly sensitive function of the pocket doping and can be significantly reduced by tuning the source elevation length ${L} _{\textsf {CV}}$ at higher pocket doping. At the same pocket conditions, a one order reduction in ${C} _{\textsf {GD}}$ is achieved with respect to the lateral configuration without compromising the intrinsic delay ( ${C} _{\textsf {GD}}\times {V} _{\textsf {DD}}/{I} _{\textsf {ON}})$ . The circuit-level investigations show that due to the, otherwise, higher ${C} _{\textsf {GD}}$ in the LTS FET, the switching delay remains unaffected by the on-current boosting caused by higher pocket doping. However, it is drastically improved by ~23% in elevated source structures at a change from $4\times 10^{\textsf {19}}$ to $5\times 10^{\textsf {19}}$ /cm3. A faster switching delay ( $\tau _{\textsf {p}}$ ) of ~116 ps is achieved at a ~33% reduced device base area.

In this paper, we present an improved high frequency small-signal distributed model for SiGe HBTs under forward-active mode based on the transmission line theory. The distributed nature of the transistor structure is taken into account in the proposed model. The single SiGe HBT is considered to be a cascade of many infinitesimal transistors, connected with the intrinsic base resistance. The closed-form solutions of admittance parameters for the distributed model are derived by solving the transmission line equation. With reasonable approximation and simplification, the model parameters are then directly extracted based on the nonlinear rational function fitting. The new improved distributed model and parameter extraction technique are validated with a $1\times 1.2\times 30\,\,\mu \text{m}^{2}$ SiGe HBT from 100 MHz to 20.89 GHz. The simulated $S$ -parameters in the proposed transmission line model are in close agreement with the measured data, and the frequency characteristics of the transistors are well predicted.

The classical astrophysical theory of Riemann ellipsoids and the quantum nuclear theory of Bohr and Mottelson share a common mathematical foundation in terms of the differential geometry of a principal bundle ${\cal P}$ and its associated vector bundle E, respectively. The bundle ${\cal P}=GL_+(3,R)$ is the connected component of the general linear group, the structure group G=SO(3) is the vorticity group, and the base manifold is the space of positive-definite real $3\times 3$ symmetricmatrices, identified geometrically with the space of inertia ellipsoids. The bundle is a Riemannian manifold whose metric is inherited from three-dimensional Euclidean space. A nonholonomic constraint force, like irrotational flow, determines a connection on the bundle.Wave functions of the Bohr-Mottelson model are sections of the associated vector bundle E = ${\cal P}\times_\rho$V, where $\rho$ denotes an irreducible representation of the vorticity group on the vector space V. Using the de Rham Laplacian $\triangle = \star d_\nabla \star d_\nabla$ for the kinetic energy introduces a "magnetic" term due to the connection between base manifold rotational and fiber vortex degrees of freedom. A class of Ehresmann connections creates a new model of nuclear rotation that predicts moments of inertia in agreement with experiment.

Given an elliptic curve E over a finite field F-q we study the finite extensions F(q)n of F-q such that the number of F(q)n-rational points on E attains the Hasse upper bound. We obtain an upper bound on the degree n for E ordinary using an estimate for linear forms in logarithms, which allows us to compute the pairs of isogeny classes of such curves and degree n for small q. Using a consequence of Schmidt's Subspace Theorem, we improve the upper bound to n

Let $\mathscr{E}\rightarrow\mathbb{P}^1_\mathbb{Q}$ be a non-trivial rational elliptic surface over $\mathbb{Q}$ with base $\mathbb{P}^1_\mathbb{Q}$ (with a section). We conjecture that any non-trivial elliptic surface has a Zariski-dense set of $\mathbb{Q}$-rational points. In this paper we work on solving the conjecture in case $\mathscr{E}$ is rational by means of geometric and analytic methods. First, we show that for $\mathscr{E}$ rational, the set $\mathscr{E}(\mathbb{Q})$ is Zariski-dense when $\mathscr{E}$ is isotrivial with non-zero $j$-invariant and when $\mathscr{E}$ is non-isotrivial with a fiber of type $II^*$, $III^*$, $IV^*$ or $I^*_m$ ($m\geq0$). We also use the parity conjecture to prove analytically the density on a certain family of isotrivial rational elliptic surfaces with $j=0$, and specify cases for which neither of our methods leads to the proof of our conjecture., Comment: 32 pages. To appear in Acta Arithmetica

Carbamates are molecules that have different types of biological activities and provide a particular chemical control against ticks. The new structures of the proposed compounds were optimized and synthetized respectively, through a molecular model using the methods:PM3, HF and DFT applying the B3LYP functional, with the basis 6-31+G(d) and 6-311+G(d,p), BVP86 and PBEPBE with 6-31+G(d) and the vibrational frequencies computed. These calculated frequencies were compared with the experimental ones to determine the most accurate level of theory for the prediction of vibrational frequencies of the compounds. The best results were obtained through HF/631+G(d). Additionally, we report a modification to obtain this type of compounds, and based on the amino-dehalogenation of ethyl chloroformate, different benzyl ethyl carbamates were synthesized modifying the base molecule. The performances obtained were compared to others already reported. The methodology used allowed us to synthesize new carbamates using benzylamine derivatives through a modification on the basic catalysis of the addition-elimination reaction.

Given a partially ordered set $P$ we study properties of topological spaces $X$ admitting a $P$-base, i.e., an indexed family $(U_\alpha)_{\alpha\in P}$ of subsets of $X\times X$ such that $U_\beta\subset U_\alpha$ for all $\alpha\le\beta$ in $P$ and for every $x\in X$ the family $(U_\alpha[x])_{\alpha\in P}$ of balls $U_\alpha[x]=\{y\in X:(x,y)\in U_\alpha\}$ is a neighborhood base at $x$. A $P$-base $(U_\alpha)_{\alpha\in P}$ for $X$ is called locally uniform if the family of entourages $(U_\alpha U_\alpha^{-1}U_\alpha)_{\alpha\in P}$ remains a $P$-base for $X$. A topological space is first-countable if and only if it has an $\omega$-base. By Moore's Metrization Theorem, a topological space is metrizable if and only if it is a $T_0$-space with a locally uniform $\omega$-base. In the paper we shall study topological spaces possessing a (locally uniform) $\omega^\omega$-base. Our results show that spaces with an $\omega^\omega$-base share some common properties with first countable spaces, in particular, many known upper bounds on the cardinality of first-countable spaces remain true for countably tight $\omega^\omega$-based topological spaces. On the other hand, topological spaces with a locally uniform $\omega^\omega$-base have many properties, typical for generalized metric spaces. Also we study Tychonoff spaces whose universal (pre- or quasi-) uniformity has an $\omega^\omega$-base and show that such spaces are close to being $\sigma$-compact., Comment: 105 pages

For a smooth curve C in $${{\mathbb {P}}}^{r_0}$$ lying on a rational surface scroll, we try to identify those complete and base point free linear series of small degree which are not obtainable just by projection from C.

This paper reports on the development, characterization, and validation of neural probes serving the growing needs of neuroscience for miniaturized tools enabling simultaneous high-resolution recording of neural activity in multiple brain areas. The probes consist of a needle-shaped shaft with a cross-section of $100\times 50\,\mu \text{m}^{2}$ and a length of 10 or 5 mm emerging from a base with dimensions of only $0.55\times 1.8$ mm2. The shafts carry 1600 and 800 recording sites, respectively, grouped into 50 (respectively 25) blocks of $4\times 8$ electrodes with an area of $17\times 17\,\mu \text{m}^{2}$ each, a pitch of 20 $\mu \text{m}$ , and an electrode-to-electrode spacing of 3 $\mu \text{m}$ . The probes are fabricated using a commercial 0.18 $\mu \text{m}$ CMOS process followed by dedicated metallization, passivation, and microfabrication steps. Neural signals are accessible through 32 analog output channels via a hierarchical digital addressing scheme implementing an advanced electronic depth control concept giving the option of multiple scanning modes and offering a switching time of 416 $\mu \text{s}$ at a clock frequency of 1 MHz. All output channels are shielded against each other, whereby crosstalk between neighboring channels is measured to be −58 dB at 1 kHz. Absolute impedance values at 1 kHz of single IrOx and Pt electrodes are $230\pm 38~\text{k}\Omega $ and $2.2\pm 0.3~\text{M}\Omega $ , respectively. In vivo recordings taking advantage of the new addressing concept for high-resolution recordings from multiple brain regions were successfully performed in anesthetized rats. [2018-0152]

Exchangeable acidity in samples from organic and mineral horizons of taiga and bog soils with strongly acid reaction (pHKCl < 3.3 and $${\text{p}}{{{\text{H}}}_{{{{{\text{H}}}_{2}}{\text{O}}}}}$$ ≤ 4.4) was determined by the Sokolov method of potentiometric titration of KCl extract before and after the addition of a sodium fluoride solution. In the same extracts, the contents of Al, Fe, and Mn ions were determined by the atomic emission method. NaF was added in an amount sufficient for binding all metal ions into fluoride complex compounds. It was found that the content of metals determined by atomic emission is lower than that calculated from titration results in 1.5–2 times in organic horizons and by 20–25% in mineral horizons. Even a higher difference between the two methods was observed for exchangeable protons: from the titration data, their content in organic horizons was 10–12% of the content determined as the difference between total exchangeable acidity and total metal ions determined by atomic emission, and 3–15% in mineral horizons. The revealed differences were attributed to the underestimated results of determining exchangeable protons in the presence of NaF, which was confirmed by the potentiometric titration of model solutions of strong and weak acids prepared from a KCl solution. It was found that the addition of NaF during the titration with a strong acid results in reaching the point of equivalence after the addition of a smaller amount of base. Reasons for the shift of the point of equivalence during titration with a strong acid in the presence of NaF require special investigations. It is recommended to estimate the exchangeable acidity of strongly acid soils due to metal ions by atomic emission or other adequate methods.

Bronsted and Lewis base catalysis of hexametalate clusters of group 5 metals [M(V)6O19]8– (M(V) = Ta, Nb) and group 6 metals [M(VI)6O19]2– (M(VI) = Mo, W) was studied using Knoevenagel condensation...