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Fix a positive integer $d$ and let $\Gamma_d$ be the class of finite groups without sections isomorphic to the alternating group $A_d$. The groups in $\Gamma_d$ were studied by Babai, Cameron and P\'{a}lfy in the 1980s and they determined bounds on the order of a primitive permutation group with this property, which have found a wide range of applications. Subsequently, results on the base sizes of such groups were also obtained. In this paper we replace the structural conditions on the group by restrictions on its point stabilizers, and we obtain similar, and sometimes stronger conclusions. For example, we prove that there is a linear function $f$ such that the base size of any finite primitive group with point stabilizers in $\Gamma_d$ is at most $f(d)$. This generalizes a recent result of the first author on primitive groups with solvable point stabilizers. For non-affine primitive groups we obtain stronger results, assuming only that stabilizers of $c$ points lie in $\Gamma_d$. We also show that if $G$ is any permutation group of degree $n$ whose $c$-point stabilizers lie in $\Gamma_d$, then $|G| \leqslant ((1+o_c(1))d/e)^{n-1}$. This asymptotically extends and improves a $d^{n-1}$ upper bound on $|G|$ obtained by Babai, Cameron and P\'{a}lfy assuming $G \in \Gamma_d$., Comment: 19 pages; to appear in Journal of Algebra (special issue in memory of Jan Saxl)

We study the natural action of S n on the set of k-subsets of the set { 1 , … , n } when 1 ≤ k ≤ n 2 . For this action we calculate the maximum size of a minimal base, the height and the maximum length of an irredundant base. Here a base is a set with trivial pointwise stabilizer, the height is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an irredundant base can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.

In this paper we prove the birational superrigidity of Fano-Mori fibre spaces $\pi\colon V\to S$, every fibre of which is a complete intersection of type $d_1\cdot d_2$ in the projective space ${\mathbb P}^{d_1+d_2}$, satisfying certain conditions of general position, under the assumption that the fibration $V/S$ is sufficiently twisted over the base (in particular, under the assumption that the $K$-condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition bounds the dimension of the base $S$ by a constant that depends on the dimension $M$ of the fibre only (as the dimension $M$ of the fibre grows, this constant grows as $\frac12 M^2$). The fibres and the variety $V$ itself may have quadratic and bi-quadratic singularities, the rank of which is bounded from below., Comment: 86 pages, the final version

Given an infinite countable discrete amenable group Γ \Gamma , we construct explicitly sharply weak mixing nonsingular Poisson Γ \Gamma -actions of each Krieger’s type: I I I λ III_\lambda , for λ ∈ [ 0 , 1 ] \lambda \in [0,1] , and I I ∞ II_\infty . The result is new even for Γ = Z \Gamma =\mathbb {Z} . As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ \Gamma -actions and infinite direct product of finite type systems of each possible Krieger’s type.

PURPOSE To measure the accuracy of the additively manufactured casts with 3 base designs: solid, honeycomb-structure, and hollowed bases. METHODS A virtual cast was used to create different base designs: solid (S Group), honeycomb-structure (HC group), and hollowed (H group). Three standard tessellation language files were used to fabricate the specimens using a material jetting printer (J720 Dental; Stratasys) and a resin (VeroDent MED670; Stratasys) (n=15). A coordinate measuring machine was selected to measure the linear and 3D discrepancies between the virtual cast and each specimen. Shapiro-Wilk test revealed that all the data was not normally distributed (P

A topological space $X$ is defined to have a neighborhood $P$-base at any $x\in X$ from some poset $P$ if there exists a neighborhood base $(U_p[x])_{p\in P}$ at $x$ such that $U_p[x]\subseteq U_{p'}[x]$ for all $p\geq p'$ in $P$. We prove that a compact space is countable, hence metrizable, if it has countable scattered height and a $\mathcal{K}(M)$-base for some separable metric space $M$. This gives a positive answer to Problem 8.6.8 in \cite{Banakh2019}. Let $A(X)$ be the free Abelian topological group on $X$. It is shown that if $Y$ is a retract of $X$ such that the free Abelian topological group $A(Y)$ has a $P$-base and $A(X/Y)$ has a $Q$-base, then $A(X)$ has a $P\times Q$-base. Also if $Y$ is a closed subspace of $X$ and $A(X)$ has a $P$-base, then $A(X/Y)$ has a $P$-base. It is shown that any Freche-Urysohn topological group with a $\mathcal{K}(M)$-base for some separable metric space $M$ is first-countable, hence metrizable. And if $P$ is a poset with calibre~$(\omega_1, \omega)$ and $G$ is a topological group with a $P$-base, then any precompact subset in G is metrizable, hence $G$ is strictly angelic. Applications in function spaces $C_p(X)$ and $C_k(X)$ are discussed. We also give an example of a topological Boolean group of character $\leq \mathfrak{d}$ such that the precompact subsets are metrizable but $G$ doesn't have an $\omega^\omega$-base if $\omega_1

A novel LDMOS featuring bulk full gate (BFG) with bulk channel and electron accumulation effect, named BFG-LDMOS, is proposed and investigated. The BFG includes bulk gate oxide (BGO) that is inserted in the ${N}$ -drift and the full gate (FG) that is formed by the wide open base transistor (P-body/ ${N}$ -drift/P + ). The gate potential is extended in the gate- ${N}$ -drift-drain (GND) region, and thus, the bulk channel of the P-body and electron accumulation effect of the ${N}$ -drift in the source- ${N}$ -drift-drain (SND) region is achieved, which significantly reduces the specific ON-resistance ( ${R}_{\text {ON,sp}}$ ). In addition, the P-body, ${N}$ -drift, and N + drain are divided by the BGO, and the P-body/ ${N}$ -drift junction (PN1) sustains the breakdown electric field for both sides, which guarantees the breakdown voltage (BV) like conventional LDMOS. The 3-D simulation results indicate that the BV and ${R}_{\text {ON,sp}}$ are 249 V and 2.93 $\text{m}\Omega \cdot $ cm 2 for the proposed BFG-LDMOS, respectively, and the Baliga’s figure of merit (FoM) is high up to 21 MW/cm 2 , which breaks through the silicon limit of the reduced surface field (RESURF).

A fundamental result of Springer says that a quadratic form over a field of characteristic ≠ 2 is isotropic if it is so after an odd degree field extension. In this paper we generalize Springer’s theorem as follows. Let R be an arbitrary semilocal ring, let S be a finite R -algebra of constant odd degree, which is etale or generated by one element, and let q be a nonsingular R -quadratic form whose base ring extension q S is isotropic. We show that then already q is isotropic.

Let $$g \geqslant 2$$ be an integer and $$S_g(n)$$ denote the sum of the digits in base g of the positive integer n. We obtain asymptotic formulas for the number of odd integers up to x that can be written as a product pq, with p, q both primes, satisfy $$S_g(p) \equiv S_g(q) \equiv a ~\mathrm{mod}\,~ b\ (b \geqslant 2, a \in {\mathbb {Z}})$$ . So, we observe a large bias amongst such integers.

We study the definability of ultrafilter bases on $$\omega $$ in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in L we can construct $$\Pi ^1_1$$ P-point and Q-point bases. We also show that the existence of a $${\varvec{\Delta }}^1_{n+1}$$ ultrafilter is equivalent to that of a $${\varvec{\Pi }}^1_n$$ ultrafilter base, for $$n \in \omega $$ . Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.

We prove that for a Hecke cuspform f ∈ S k ( Γ 0 ( N ) , χ ) and a prime l > max ⁡ { k , 6 } such that l ∤ N , there exists an infinite family { k r } r ≥ 1 ⊆ Z such that for each k r , there is a cusp form f k r ∈ S k r ( Γ 0 ( N ) , χ ) such that the Deligne representation ρ f k r , l is a crystalline and potentially diagonalizable lift of ρ ‾ f , l . When f is l-ordinary, we base our proof on the theory of Hida families, while in the non-ordinary case, we adapt a local-to-global argument due to Khare and Wintenberger in the setting of their proof of Serre's modularity conjecture, together with a result on existence of lifts with prescribed local conditions over CM fields, a flatness result due to Bockle and a local dimension result by Kisin. We discuss the motivation and tentative future applications of our result in ongoing research on the automorphy of GL 2 n -type representations in the higher level case.

3C 84 (NGC 1275) is the radio source at the centre of the Perseus cluster and exhibits a bright radio jet. We observed the source with the Global Millimeter VLBI Array (GMVA) between 2008 and 2015, with a typical angular resolution of ∼50 μas. The observations revealed a consistent double nuclear structure separated by ∼770 gravitational radii assuming a black hole mass of 3.2 × 108 M⊙. The region is likely too broad and bright to be the true jet base anchored in the accretion disc or black hole ergosphere. A cone and parabola were fit to the stacked (time averaged) image of the nuclear region. The data did not strongly prefer either fit, but combined with a jet/counter-jet ratio analysis, an upper limit on the viewing angle to the inner jet region of ≤35° was found. This provides evidence for a variation of the viewing angle along the jet (and therefore a bent jet) within ∼0.5 pc of the jet launching region. In the case of a conical jet, the apex is located ∼2400 gravitational radii upstream of the bright nuclear region and up to ∼600 gravitational radii upstream in the parabolic case. We found a possible correlation between the brightness temperature and relative position angle of the double nuclear components, which may indicate rotation within the jet. © 2021 The Author(s)., This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1A6A3A01086420). JAH was supported by Korea Research Fellowship Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT, South Korea (2018H1D3A1A02032824) and the research grant (2021R1C1C1009973). S-SL was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MIST) (2020R1A2C2009003). J-YK is supported for this research by the International Max-Planck Research School (IMPRS) for Astronomy and Astrophysics at the University of Bonn and Cologne. This research was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Universities Space Research Association through a contract with NASA. RL acknowledges the support of the Spanish Ministerio de Economía y Competitividad (grant PID2019-108995GB-C21), the Consejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía (grant P18-FR-1769), and the Consejo Superior de Investigaciones Científicas (grant 2019AEP112). GFP is supported for this research by the International Max-Planck Research School (IMPRS) for Astronomy and Astrophysics at the University of Bonn and Cologne. ST and MK acknowledge support via NRF grant 2019R1F1A1059721. This research has made use of data obtained with the Global Millimeter VLBI Array (GMVA), which consists of telescopes operated by the MPIfR, IRAM, Onsala, Metsahovi, Yebes, the Korean VLBI Network, the Green Bank Observatory, and the Very Long Baseline Array (VLBA). The VLBA is an instrument of the NRAO, which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The data were correlated at the correlator of the Max Planck Institute for Radioastronomy (MPIfR) in Bonn, Germany. This work made use of the Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under licence., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

Let $R = \oplus _{n\in \mathbb {N}_{0}}R_{n}$ be a Noetherian homogeneous ring with irrelevant ideal $R_{+} = \oplus _{n\in \mathbb {N}} R_{n}$ and with local base ring $(R_{0},\mathfrak {m}_{0})$ . Let M, N be two finitely generated $\mathbb {Z}$ -graded R-modules. We show that the lengths of the graded components of various graded submodules and quotients of the i-th generalized local cohomology $H^{i}_{R_{+}}(M, N)$ are anti-polynomial. Under some mild assumptions, the Artinianness of $H^{i}_{R_{+}}(M, N)$ and the asymptotic behavior of the R0-modules $H^{i}_{R_{+}}(M, N)_{n}$ for $n\rightarrow -\infty $ in the range $i\leq \inf \{i\in \mathbb {N}_{0} \vert \sharp \{n\vert \ell _{R_{0}}$ $(H^{i}_{ R_{+}}(M , N)_{n}) = \infty \}=\infty \}$ will be studied. Moreover, it has been proved that, if u is the least integer i for which $H^{i}_{R_{+}}(M,N)$ is not Artinian and $\mathfrak {q}_{0}$ is an $\mathfrak {m}_{0}$ -primary ideal of R0, then $H^{u}_{R_{+}}(M,N)/\mathfrak q_{0}H^{u}_{R_{+}}(M,$ N) is Artinian with Hilbert-Kirby polynomial of degree less than u. In particular, with M = R, we deduce the correspondent result for ordinary local cohomology module $H^{i}_{R_{+}}(N)$ .

Large gains in surface hardness and corrosion resistance of EN41B have been achieved for the AS_PN process. However, the effect of the AS_PN process parameters, like treatment time and temperature, on the hardness, corrosion, and wear of EN41B have not been investigated. Thus, in this study, EN41B samples have been treated at 500 °C and 550 °C for 2 h, 4 h and 6 h with a gas flow ratio of $${\text{H}}_{2} /{\text{N}}_{2} = 4:1$$ . Scanning electron microscopy analysis showed that the compound layers varied from 15.251 µm to 25.045 µm, and also revealed the formation of transformed austenite phases. X-ray diffraction analysis has revealed the formation of $$\varepsilon - {\text{Fe}}_{2 - 3} {\text{N}}$$ and $$\gamma^{\prime} - {\text{Fe}}_{4} {\text{N}}$$ phases on the surface of the samples. The microhardness test has revealed that the maximum gain in the hardness after treatment is 4.2 times that of the base material. Finally, it was observed from potentiodynamic polarization testing that the sample treated at 550 °C for 6 h has a minimum corrosion rate of 419.10 mm/year ×10−3.

Let $$s_{q}$$ denote the sum of digits function in base q. The aim of this work is to estimate the exponential sums involving the sum of digits of shifted integers, namely of the form $$\displaystyle \sum \nolimits _{n\leqslant x}e(\alpha _{0}s_{q}(n)+ \cdots +\alpha _{k}s_{q}(n+k))$$ , where k is a nonnegative integer and $$\alpha _{0},\ldots ,\alpha _{k}$$ are real numbers. We deduce from these estimates some results concerning the correlation of the Thue–Morse sequence.

We answer the question by Matt Brin on the structure of diagram groups over semigroup presentation ${\mathcal P}=\langle a,b,c\mid a=bc,b=ca,c=ab\rangle$. In the talk on Oberwolfach workshop, Brin conjectured that the diagram group over $\mathcal P$ with base $a$ is isomorphic to the generalized Thompson's group $F_9$. We confirm this conjecture and consider some generalizations of this fact., Comment: arXiv admin note: text overlap with arXiv:math/0211396

A three-dimensional (3D) FBG accelerometer was proposed by installing three FBGs in an integrated oscillator structure which consists of two pairs of flexible hinges, a thin cylinder mass block and a base. The theoretical model of the proposed 3D accelerometer was established, and the dynamic response characteristics of the 3D accelerometer with optimal structural parameters were simulated using finite element software. Lots of sensing tests were finished and the sensing data showed that the sensitivities of the proposed 3D accelerometer in X-, Y-, and Z-directions are 108.7 pm/g, 144.2 pm/g, and 27.9 pm/g respectively, the working frequency range in X- and Y- directions are 40 – 300 Hz, and the acceleration amplitude range is 1 – 10 g. The proposed 3D accelerometer has the advantages of small size (28 mm $\times38$ mm $\times38$ mm), light weight (42 g), and simultaneous measurement of multi-dimensional acceleration.

Calorimetry is used to measure the heats of interaction between an L-glutathione solution and HNO3 solutions at a temperature of 298.15 K and ionic strengths of 0.5, 1.0, and 1.5 М (KNO3 background electrolyte). Literature data on the stepwise dissociation constants of L-glutathione are extrapolated to zero ionic strength. Values $${\text{p}}K_{1}^{0}$$ = 2.05 ± 0.03, $${\text{p}}K_{2}^{0}$$ = 3.49 ± 0.03, $${\text{p}}K_{3}^{0}$$ = 8.65 ± 0.05, and $${\text{p}}K_{4}^{0}$$ = 9.60 ± 0.05 are obtained and the stepwise peptide ionization constants at fixed ionic strength values are calculated (I = 0.5, 1.0, 1.5 М). The values of the heat of dissociation of the tripeptide are calculated using the universal HEAT program. Standard thermodynamic characteristics (ΔrH°, ΔrG°, and ΔrS°) of reactions of acid–base interaction in L-glutathione aqueous solutions are calculated. The effect the concentration of the background electrolyte has on the enthalpy of peptide dissociation is considered.

A time-division duplex (TDD) transmit/receive (T/R) millimeter-wave (mm-wave) front-end in 0.13- $\mu \text{m}$ SiGe BiCMOS for fifth generation (5G) is presented. The front-end is composed of a power amplifier (PA), a low noise amplifier (LNA), and a single-pole double-throw (SPDT) switch. At mm-wave bands, the traditional SPDT switch limits the output power of the front-end in transmit mode. In this article, an asymmetric SPDT switch is proposed with high-power-handling capability (simulated OP $_{\mathrm {1\,dB}} > 28$ dBm), low insertion loss, and compact structure at 24–30 GHz. A balanced architecture is used to implement a high gain and high linearity PA with excellent input/output return losses and load-variation insensitivity. The effect of the feedback capacitor in the base of the cascode stage has been analyzed. The standalone PA achieves OP $_{\mathrm {1\,dB}}$ /peak $\text {PAE} > 16.9$ dBm/18.7% across 24–30 GHz and the OP $_{\mathrm {1\,dB}}$ /peak PAE still exceeds >15.9 dBm/16.3% including the switch loss and compression. 5G NR FR2 64-QAM modulation tests demonstrate the high linearity of the balanced PA. At 28 GHz, the standalone PA shows the EVM of −29.93 dB/−26.06 dB with an average output power ( $P_{\mathrm {avg}}$ ) of 10.15 dBm/12.16 dBm. The front-end in transmit mode shows the EVM of −29.63 dB/−26.02 dB with an average output power of 7.76 dBm/9.59 dBm. A wideband LNA is designed and exhibits a measured gain of 26 dB with a 3-dB bandwidth of 19–35 GHz, a noise figure (NF) < 5.3 dB at 24–30 GHz including the switch loss. The proposed front-end achieves high linearity in transmit mode and low NF in receive mode.

A famous result of Christol gives that a power series $$F(t)=\sum _{n\ge 0} f(n)t^n$$ with coefficients in a finite field $$\mathbb {F}_q$$ of characteristic p is algebraic over the field of rational functions in t if and only if there is a finite-state automaton accepting the base-p digits of n as input and giving f(n) as output for every $$n\ge 0$$ . An extension of Christol’s theorem, giving a complete description of the algebraic closure of $$\mathbb {F}_q(t)$$ , was later given by Kedlaya. When one looks at the support of an algebraic power series, that is the set of n for which $$f(n)\ne 0$$ , a well-known dichotomy for sets generated by finite-state automata shows that the support set is either sparse—with the number of $$n\le x$$ for which $$f(n)\ne 0$$ bounded by a polynomial in $$\log (x)$$ —or it is reasonably large in the sense that the number of $$n\le x$$ with $$f(n)\ne 0$$ grows faster than $$x^{\alpha }$$ for some positive $$\alpha $$ . The collection of algebraic power series with sparse supports forms a ring and we give a purely algebraic characterization of this ring in terms of Artin–Schreier extensions and we extend this to the context of Kedlaya’s work on generalized power series.

Sufficient and necessary conditions are provided on warped product manifolds and their base and fiber manifolds for a vector field $$\varphi _{j}$$ to be a $$\varphi \left( \mathrm {Ric}\right) $$ -vector field , that is, $$\nabla _{i}\varphi _{j}=\mu R_{ij}$$ where $$R_{ij}$$ is the Ricci tensor of M and $$ \mu $$ is a scalar. Two warped product space-times admitting $$\varphi \left( \mathrm {Ric}\right) $$ -vector fields are considered. Lorentzian quasi-Einstein manifolds admitting a time-like $$\varphi \left( \mathrm {Ric} \right) $$ -vector field are shown to be either Ricci simple or a perfect fluid GRW space-time. The generators of a Lorentzian generalized quasi-Einstein manifold admitting a time-like $$\varphi \left( \mathrm {Ric} \right) $$ -vector field are eigenvectors of the Ricci tensor with zero eigenvalue.

Number pyramids are common in elementary school mathematics. Trying to express the value of the top block in terms of the values at the base leads to the binomial coefficients. It also seems natural to ask for the maximal number of odd numbers in a number pyramid of a given size. The answer is easy to state, but the proof is nontrivial: A $$k$$ k step number pyramid can have at most $$\left\lfloor\frac{k(k+1)+1}{3}\right\rfloor$$ k ( k + 1 ) + 1 3 odd numbers, which equals two thirds of the number of blocks rounded to the nearest integer. All maximal and almost maximal solutions are given explicitly. To this end, we rephrase the question in terms of colored tilings. In the outlook we present relations to other—mostly geometric—subjects and problems.

Fluid flow and heat transfer of $$\text {Al}_2\text {O}_3$$ /water and CuO/water nanofluids with 1–3 $$\%$$ volume fraction of nanoparticle in a clockwise–counter-clockwise twisted square duct $$(T_{CW-CCW}SD)$$ are numerically simulated using the $$\kappa --\epsilon $$ turbulence model. Nanofluids flow through a twisted duct with uniform wall temperature boundary conditions, twist ratios of 8.5, 11.5, 16.5 and Reynolds numbers of 100–20,000 are studied numerically. The results show that reducing twist ratios from 16.5 to 8.5 improves heat transfer significantly. In comparison with the results obtained using simple base water, the average percentage increase in Nusselt number is around 0.1–0.5 $$\%$$ higher at 1 $$\%$$ volume concentration of $$\text {Al}_2\text {O}_3$$ nanoparticle and 0.5–1 $$\%$$ increment in average Nusselt number is observed for 1 $$\%$$ concentration of CuO. It was also discovered that increasing the concentration of $$\text {Al}_2\text {O}_3$$ nanoparticle in normal water from 2–3% reduces heat transfer enhancement, whereas the CuO nanoparticle enhances heat transfer coefficient for the same volume fraction of nanoparticle, and this enhancement is found to be within 0.5%. To compare twisted and straight ducts, an enhancement factor or quantity is calculated based on constant pumping power criteria. The enhancement factor is used to prioritize the twisted square duct selections. Performance evaluation criteria show that the twisted duct performs well up to the Reynolds number of 2000, while beyond the Reynolds of 2000, this twisted duct is not suitable due to strong presence of reverse flow. It is recommended to use twisted clockwise–counter-clockwise square duct for the Reynolds number till 2000. Correlations involving swirl parameters such as twist ratios, percentage of volume fraction of nanoparticles and Reynolds number are also proposed separately for friction factor and Nusselt number.

Visible-light heterojunction phototransistors (HPTs) featuring high responsivity, high speed, and bias-controlled spectral response were fabricated using dopant-free polarization induced p-type base and InGaN(4 nm)/GaN(1.8 nm) superlattice (SL) absorber. Under 402-nm illumination of 0.16 mW/cm2, the fabricated HPTs exhibited a high photocurrent to dark current ( ${I}_{\text {ph}} / {I}_{\text {dark}}$ ) ratio of ${8} \times {10} ^{{4}}$ and a responsivity of 37 A/W at 1 V. The responsivity reaches 470 A/W at 3 V and the ${I}_{\text {ph}} / {I}_{\text {dark}}$ ratio is ~3.0. A high response speed with a rise time of ~3.4 ns was acquired. Moreover, due to the polarization effect in the SLs, the HPTs show bias-controlled wavelength selectivity without optical filter: narrowband response from 362 to 440 nm at bias ≤ 1.0 V, and broadband response below 440 nm at bias ≥1.5 V.

Let $$\Gamma $$ be a finite tree. Fix a base vertex $$x_0$$ of $$\Gamma $$ and let $$T=T^{(x_0)}$$ be the Terwilliger algebra of $$\Gamma $$ with respect to $$x_0$$ . Denote by H the group of automorphisms of $$\Gamma $$ that fix $$x_0$$ , and let $$S={\mathrm{End}}_H~(V)$$ be the centralizer algebra of H, where $$V={\mathbb {C}}X$$ is the standard module of T with X the underlying vertex set of $$\Gamma $$ . It is obvious that T is contained in S. We show how large the gap is between T and S by comparing irreducible representations of them; in particular we find precisely when $$T=S$$ holds.

In this paper we investigate combinatorial constructions for $w$-cyclic holely group divisible packings with block size three (briefly by $3$-HGDPs). For any positive integers $u,v,w$ with $u\equiv0,1~(\bmod~3)$, the exact number of base blocks of a maximum $w$-cyclic $3$-HGDP of type $(u,w^v)$ is determined. This result is used to determine the exact number of codewords in a maximum three-dimensional $(u\times v\times w,3,1)$ optical orthogonal code with at most one optical pulse per spatial plane and per wavelength plane.

This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid $$f^{\prime}\left( \xi \right),g\left( \xi \right)$$ f ′ ξ , g ξ are decayed for high values of $$\phi_{1} ,\phi_{2} ,\,Fr$$ ϕ 1 , ϕ 2 , F r and $$k_{1}$$ k 1 factors.

Vertical biristors are small footprint ( ${4}{F}^{{2}}$ ) floating base bipolar junction transistors (BJTs) proposed for high-speed volatile memory applications. One key challenge is (i) the high latch-up voltage with Si-based biristors because of the high threshold of impact ionization (II) in Si. In this article, an epitaxial ${n}^{+}/{i}/{\delta {p}}^{+}/{i}/{n}^{+}$ -based vertical biristor is proposed with an asymmetric doping profile that enables sub-bandgap II only in the negative polarity. First, in the negative polarity, a latch-up voltage as low as 0.5 V due to sub-bandgap II is demonstrated. Faster programming with higher bias is observed. Second, erase is demonstrated in the positive bias, where II is insignificant. Overall, a large read window ( ${\Delta } {I}=\text {0.01 mA}$ ) with a low variability ( ${\sigma /\mu }$ in ${\Delta }{I}$ ) for cycle-to-cycle (C2C $1 {\mu }\text{s}$ is observed, taking into account C2C and D2D variations. A high endurance (> 107cycles) is also observed. Therefore, asymmetrically doped vertical biristor is promising for very low voltage high speed memory application compared to dynamic random access memory (DRAM).

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. As another application of these descent theoretic methods, we compute the cellular Picard group of 2-complete Hermitian $K$-theory over $\mathop{Spec}(\mathbb{C})$, showing that the only invertible cellular spectra are suspensions of the tensor unit., Comment: v4: results made unconditional, assumptions on base scheme weakened. Version to appear in Annals of K-theory

Twisted generalized Weyl algebras (TGWAs) $A(R,\sigma,t)$ are defined over a base ring $R$ by parameters $\sigma$ and $t$, where $\sigma$ is an $n$-tuple of automorphisms, and $t$ is an $n$-tuple of elements in the center of $R$. We show that, for fixed $R$ and $\sigma$, there is a natural algebra map $A(R,\sigma,tt')\to A(R,\sigma,t)\otimes_R A(R,\sigma,t')$. This gives a tensor product operation on modules, inducing a ring structure on the direct sum (over all $t$) of the Grothendieck groups of the categories of weight modules for $A(R,\sigma,t)$. We give presentations of these Grothendieck rings for $n=1,2$, when $R=\mathbb{C}[z]$. As a consequence, for $n=1$, any indecomposable module for a TGWA can be written as a tensor product of indecomposable modules over the usual Weyl algebra. In particular, any finite-dimensional simple module over $\mathfrak{sl}_2$ is a tensor product of two Weyl algebra modules., Comment: 31 pages, 3 figures

We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field $k$ of characteristic $p>5$. We also show the log abundance conjecture for threefolds over $k$ when the nef dimension is not maximal, and the base point free theorem for threefolds over the algebraic closure of any finite field of characteristic $p>2$., 33 pages; the article has been substantially changed and the results are stronger: we now show log non-vanishing for all three-dimensional klt pairs of characteristic $p>5$, and log abundance when the nef dimension is not maximal. Further, we corrected a mistake in Lemma 4.3(1) (now Lemma 5.1(1)): the effectivity of adjoint divisors on surfaces holds only up to numerical equivalence

Precise attitude control of space manipulators plays an important role in advanced on-orbit assembly tasks. The vibration of flexible appendage and inertial uncertainties encountered in the operating process, however, may cause attitude error or even safety threats to the space manipulator system. In this article, a high-precision attitude control scheme of a space manipulator system is designed via a combination of disturbance observer (DO), prescribed performance-based ${H} _{\infty }$ control, and iterative learning control (ILC) techniques. The proposed control scheme consists of three portions: 1) a DO that estimates the vibration disturbance caused by flexible appendage of base satellite; 2) a robust ${H} _{\infty }$ controller with prescribed performance to attenuate the inertial uncertainties resulting from capture of an unknown object; and 3) an ILC for improving the transient and steady-state process in the presence of a repetitive on-orbit assembly task. This novel control scheme can not only handle the flexible vibration and inertial uncertainty of the space manipulator but also achieve satisfactory tracking performance. Both simulation and experimental results confirm the superiority of the proposed control strategy.

We compare the homology of a congruence subgroup Gamma of GL_2(Z) with coefficients in the Steinberg modules over Q and over E, where E is a real quadratic field. If R is any commutative base ring, the last connecting homomorphism psi_{Gamma,E} in the long exact sequence of homology stemming from this comparison has image in H_0(Gamma, St(Q^2;R)) generated by classes z_\beta indexed by beta in E \ Q. We investigate this image. When R=C, H_0(Gamma, St(Q^2;C)) is isomorphic to a space of classical modular forms of weight 2, and the image lies inside the cuspidal part. In this case, z_beta is closely related to periods of modular forms over the geodesic in the upper half plane from beta to its conjugate beta'. Assuming GRH we prove that the image of $\psi_{\Gamma,E}$ equals the entire cuspidal part. When R=Z, we have an integral version of the situation. We define the cuspidal part of the Steinberg homology, H_0^cusp(Gamma, St(Q^2;Z)). Assuming GRH we prove that for any congruence subgroup, psi_{Gamma,E} always has finite index in H_0^cusp(Gamma, St(Q^2;Z)), and if Gamma=Gamma_1(N)^pm or \Gamma_1(N), then the image is all of H_0^cusp(Gamma, St(Q^2;Z)). If Gamma=Gamma_0(N)^pm or Gamma_0(N), we prove (still assuming GRH) an upper bound for the size of H_0^cusp(Gamma, St(Q^2;Z))/image(psi_{Gamma,E}). We conjecture that the results in this paragraph are true unconditionally. We also report on extensive computations of the image of psi_{Gamma,E} that we made for Gamma=Gamma_0(N)^pm and Gamma=Gamma_0(N). Based on these computations, we believe that the image of psi_{Gamma,E} is not all of H_0^cusp(Gamma, St(Q^2;Z)) for these groups, for general N., Comment: 37 pages, 2 tables

Purpose: To analyze the differences in the force–velocity (F–v) profile assessed under unconstrained (ie, using free weights) and constrained (ie, on a Smith machine) vertical jumps, as well as to determine the between-day reliability. Methods: A total of 23 trained participants (18 [1] y) performed an incremental load squat jump test (with ∼35%, 45%, 60%, and 70% of the subjects’ body mass) on 2 different days using free weights and a Smith machine. Nine of these participants repeated the tests on 2 other days for an exploratory analysis of between-day reliability. F–v variables (ie, maximum theoretical force [F0], velocity [v0], and power, and the imbalance between the actual and the theoretically optimal F–v profile) were computed from jump height. Results: A poor agreement was observed between the F–v variables assessed under constrained and unconstrained conditions (intraclass correlation coefficient [ICC] .70). The F–v variables computed under constrained conditions showed an overall good agreement (ICC = .75–.95 for all variables) and no significant differences between days (P > .05), but a high variability for v0, the imbalance between the actual and the theoretically optimal F–v profile, and maximal theoretical power (coefficient of variation = 17.0%–27.4%). No between-day differences were observed for any F–v variable assessed under unconstrained conditions (P > .05), but all of the variables presented a low between-day reliability (coefficient of variation > 10% and ICC Conclusions: F–v variables differed meaningfully when obtained from constrained and unconstrained loaded jumps, and most importantly seemed to present a low between-day reliability.

We present multi-wavelength fast timing observations of the black hole X-ray binary MAXI J1820+070 (ASASSN-18ey), taken with the Karl G. Jansky Very Large Array (VLA), Atacama Large Millimeter/Sub-Millimeter Array (ALMA), Very Large Telescope (VLT), New Technology Telescope (NTT), Neutron Star Interior Composition Explorer (NICER), and XMM-Newton. Our data set simultaneously samples ten different electromagnetic bands (radio - X-ray) over a 7-hour period during the hard state of the 2018-2019 outburst. The emission we observe is highly variable, displaying multiple rapid flaring episodes. To characterize the variability properties in our data, we implemented a combination of cross-correlation and Fourier analyses. We find that the emission is highly correlated between different bands, measuring time-lags ranging from hundreds of milliseconds between the X-ray/optical bands to minutes between the radio/sub-mm bands. Our Fourier analysis also revealed, for the first time in a black hole X-ray binary, an evolving power spectral shape with electromagnetic frequency. Through modelling these variability properties, we find that MAXI J1820+070 launches a highly relativistic ($\Gamma=6.81^{+1.06}_{-1.15}$) and confined ($\phi=0.45^{+0.13}_{-0.11}$ deg) jet, which is carrying a significant amount of power away from the system (equivalent to $\sim0.6 \, L_{1-100{\rm keV}}$). We additionally place constraints on the jet composition and magnetic field strength in the innermost jet base region. Overall, this work demonstrates that time-domain analysis is a powerful diagnostic tool for probing jet physics, where we can accurately measure jet properties with time-domain measurements alone., Comment: 23 pages, 16 figures, accepted to MNRAS

Infinitely generated closed classes $$\Pi_{1}{-}\Pi_{4}$$ of 01-functions of three-valued logic are investigated. The property of maximality is proved for classes $$\Pi_{3}$$ and $$\Pi_{4}$$ . Each proper extension of classes leads to finitely generated closed classes. It is proved that there is no base in class $$\Pi_{1}$$ . All of the simplest two- and three-variable functions obtainable by superposition from an arbitrary function not belonging to class $$\Pi_{1}$$ are found.

Let $$(F_{n})$$ be the sequence of Fibonacci numbers defined by $$F_{0}=0,~F_{1}=1$$ , and $$F_{n}=F_{n-1}+F_{n-2}$$ for $$n\ge 2.$$ Let $$2\le m\le n$$ and $$b=2,3,4,5,6,7,8,9.$$ In this study, we show that if $$F_{m}F_{n}$$ is a repdigit in base b and has at least two digits, then $$\begin{aligned} F_{m}F_{n}\in \left\{ 3,4,5,6,8,9,10,13,15,16,21,24,26,40,42,63,170,273\right\} . \end{aligned}$$ Furthermore, it is shown that if $$F_{n}$$ is a repdigit in base b and has at least two digits, then $$\begin{aligned} (n,b)=(7,3),(8,4),(8,6),(4,2),(5,4),(6,3),(6,7). \end{aligned}$$

Let $$q \geq 2$$ be an integer and let $$s_{q}(n)$$ be the sum-of-digits function in base q of the positive integer n. In this paper we obtain asymptotic formulae for the distribution of $$(s_q(n^2 {\rm mod} q^k))_{n 2$$ is a prime. Furthermore, we give exact identities for the distribution of $$(s_p(n^{d} {\rm mod} p^k))_{n

Given a real number x > 0 x>0 , we determine q s ( x ) ≔ inf ⁡ U ( x ) q_s(x)≔\operatorname {inf}{\mathscr {U}}(x) , where U ( x ) {\mathscr {U}}(x) is the set of all bases q ∈ ( 1 , 2 ] q\in (1,2] for which x x has a unique expansion of 0 0 ’s and 1 1 ’s. We give an explicit description of q s ( x ) q_s(x) for several regions of x x -values. For others, we present an efficient algorithm to determine q s ( x ) q_s(x) and the lexicographically smallest unique expansion of x x . We show that the infimum is attained for almost all x x , but there is also a set of points of positive Hausdorff dimension for which the infimum is proper. In addition, we show that the function q s q_s is right-continuous with left-hand limits and no downward jumps, and characterize the points of discontinuity of q s q_s . A large part of the paper is devoted to the level sets L ( q ) ≔ { x > 0 : q s ( x ) = q } L(q)≔\{x>0:q_s(x)=q\} . We show that L ( q ) L(q) is finite for almost every q q , but there are also infinitely many infinite level sets. In particular, for the Komornik-Loreti constant q K L = min ⁡ U ( 1 ) ≈ 1.787 q_{KL}=\operatorname {min}{\mathscr {U}}(1)\approx 1.787 we prove that L ( q K L ) L(q_{KL}) has both infinitely many left- and infinitely many right accumulation points.

Active screen plasma nitriding is a newly developed technique utilized to enhance low alloy steel's surface property by placing them inside a steel case and supplying biased voltage to the cage. In this work, low alloy steel EN24 samples are plasma nitrided using active screen at different process parameters to improve its surface properties. The EN24 samples are treated at 500˚C and 550˚C treatment temperature for 2 h, 4 h and 6 h with gas flow ratio of $${H}_{2}/{N}_{2}=4:1$$ .The active screen plasma-nitrided samples are analyzed with various analytical techniques such as SEM, XRD, EDS, microhardness test, weight loss technique and potentiodynamic polarization test. From the SEM analysis, it is found that the compound layers vary from 12.680 to 22.025 µm. Further, the SEM analysis also reveals the formation of transformed austenite phases with increasing temperature and treatment time. Phase identification is performed on treated samples by XRD, which reveals the formation of $$\varepsilon ({Fe}_{2-3}N)$$ and $$\upgamma ({Fe}_{4}N)$$ on the surface of the samples. Using the microhardness test, it is found that the hardness value of treated samples has increased by 3.5 times (approx.) from the base material. From the weight loss technique, the minimum weight loss is seen for the treated sample at 500˚C for 6 h. Finally, it is observed from the potentiodynamic polarization test of the sample treated at 550˚C for 6 h has the minimum corrosion rate of 446.20 mm/year × 10−3.

Mutually unbiased bases (MUBs), a kind of important best measurement base, is widely applied to quantum information processing. In this paper, we obtain the different unextendible maximally entangled bases (UMEBs) by constructing unitary matrices in bipartite systems HCode $C^{d}\otimes C^{d^{\prime }}(\frac {d^{\prime }}{2}< d< d^{\prime })$ . Then, we show that the sufficient and necessary conditions for UMEBs extend to MUBs in this bipartite systems. Finally, these results are generalized in bipartite systems $C^{d}\otimes C^{d^{\prime }}(d^{\prime }=qd+r,\ 0

A locally convex space (lcs) E is said to have an $$\omega ^{\omega }$$ ω ω -base if E has a neighborhood base $$\{U_{\alpha }:\alpha \in \omega ^\omega \}$$ { U α : α ∈ ω ω } at zero such that $$U_{\beta }\subseteq U_{\alpha }$$ U β ⊆ U α for all $$\alpha \le \beta $$ α ≤ β . The class of lcs with an $$\omega ^{\omega }$$ ω ω -base is large, among others contains all (LM)-spaces (hence (LF)-spaces), strong duals of distinguished Fréchet lcs (hence spaces of distributions $$D^{\prime }(\Omega )$$ D ′ ( Ω ) ). A remarkable result of Cascales-Orihuela states that every compact set in an lcs with an $$\omega ^{\omega }$$ ω ω -base is metrizable. Our main result shows that every uncountable-dimensional lcs with an $$\omega ^{\omega }$$ ω ω -base contains an infinite-dimensional metrizable compact subset. On the other hand, the countable-dimensional vector space $$\varphi $$ φ endowed with the finest locally convex topology has an $$\omega ^\omega $$ ω ω -base but contains no infinite-dimensional compact subsets. It turns out that $$\varphi $$ φ is a unique infinite-dimensional locally convex space which is a $$k_{\mathbb {R}}$$ k R -space containing no infinite-dimensional compact subsets. Applications to spaces $$C_{p}(X)$$ C p ( X ) are provided.

Balanced incomplete block design (BIBD) offers an important way to construct non-homogeneous quantum low-density-parity-check (LDPC) codes of Calderbank-Shor-Steane (CSS) type. However, the rates of the quantum codes based on this method are limited to be $1-2/m$ approximately, where $m$ , the number of base blocks chosen from the associated BIBD, is even. We overcome this limitation by providing a rate scalable way to construct non-homogeneous quantum LDPC codes of CSS type. With our method, the rates of the resultant quantum codes are $1-2/m'$ , where $m'=m/e$ and $e\in \{1, 2\}$ . Note that here $m'$ can be odd . Thus, we double the rate range of the codes yielded from the existing strategies. Moreover, one can switch codes between the two rates flexibly adapting to various application scenarios.

Some alloys such as many Cr-based systems show mass gain discontinuities during thermogravimetric measurements which strongly affect the oxidation kinetics. The behaviour cannot be described by the current models available in the literature. Thus, a novel $$k_\mathrm{para}$$ k para –$$k_\mathrm{lin}$$ k lin -P-model was developed to describe oxidation kinetics during the isothermal exposure of materials which show such behaviour. Beside the parabolic rate constant $$k_\mathrm{para}$$ k para and the linear mass loss constant $$k_\mathrm{lin}$$ k lin , the P-value and $$f_P$$ f P are introduced to take into account spontaneous rapid mass gains due to local oxide scale failure. The parameter P serves as a measure for the mass gain due to discontinuous events and $$f_P$$ f P is the frequency of such events. The both parameters can be related to oxide scale detachment and growth stresses. The application of the model is demonstrated for the oxidation of Cr–Si-based alloys in synthetic air at $$1200^{\circ }\hbox {C}$$ 1200 ∘ C for 100 h. For these alloys, the origin of the mass gain discontinuities is discussed and the meaning of P and $$f_P$$ f P is explained in more detail. Using this newly developed model, an insight into growth and nitridation resistance of oxide scales as well as scale adhesion is gained.

This paper demonstrates the advantages of stochastic design optimization on a passenger car diesel engine: the emission distribution in the vehicle fleet can be significantly reduced by optimizing the base engine calibration taking into account component tolerances. This paper is an extension to the work presented in [25]. The conventional calibration approach of using empirical safety coefficients is replaced by explicitly taking into account the uncertainty stemming from manufacturing tolerances. The method enables us to treat low-emission spread in a fleet as an optimization target. This process enables a more robust design and helps to avoid recalibration steps that potentially generate high costs. The method consists of four steps: an initial uncertainty analysis, which accounts for engine component tolerances and determines the underlying parameter uncertainty of the engine model—with parameter uncertainty being deviations in the model parameters resulting from component tolerances. Followed by a measurement campaign according to the design of experiments principles, the training of a stochastic engine model and the solving a stochastic optimization problem. The latter two are discussed in more detail. First, the stochastic models are validated on transient testbed measurements with different setups, which are subject to uncertainty. The model error for both engine-out particulate matter and nitrogen oxides ( $${\text{NO}}_{{ x}}$$ ) is extremely low. Then, stochastic optimization is performed on a calibration task aiming to minimize engine-out PM for the entire fleet while ensuring that the $${\text{NO}}_{{ x}}$$ emission remains below a given upper threshold, again for the entire fleet. Boundary constraints and smoothness constraints are employed to ensure feasibility and smooth engine maps. The optimization results are compared to the original calibration of the test engine—both for a representative nominal engine and the expected fleet behavior. The results show a significant improvement in engine-out PM while complying with the imposed constraints, including the $${\text{NO}}_{{ x}}$$ emission limit for the entire fleet.

In the present paper, we extend the study of (Ali et al. in J. Inequal. Appl. 2020:241, 2020) by using differential equations (García-Río et al. in J. Differ. Equ. 194(2):287–299, 2003; Pigola et al. in Math. Z. 268:777–790, 2011; Tanno in J. Math. Soc. Jpn. 30(3):509–531, 1978; Tashiro in Trans. Am. Math. Soc. 117:251–275, 1965), and we find some necessary conditions for the base of warped product submanifolds of cosymplectic space form $\widetilde{M}^{2m+1}(\epsilon )$ M ˜ 2 m + 1 ( ϵ ) to be isometric to the Euclidean space $\mathbb{R}^{n}$ R n or a warped product of complete manifold N and Euclidean space $\mathbb{R}$ R .

In this letter, a novel spatial parallel continuum robot is proposed. It is composed of three tendon-actuated continuum robots as kinematic chains that are coupled at a common end-effector platform by spherical joints. A modular design approach is used, allowing the reconfiguration of each continuum robot's base position and orientation to adapt the overall structure to application specific constraints and environments. The parallel continuum robot is evaluated in terms of its position and orientation repeatability. Furthermore, comparisons are made to the performance of the single continuum kinematic chains. Overall, average position and orientation repeatabilities of 3.3 mm and 1.2 $^{\circ }$ can be achieved for the parallel continuum robot, with a single individual continuum segment showing repeatabilities of 5.5 mm and 3.2 $^{\circ }$ . The proposed parallel continuum robot exhibits improved repeatabilities than each of the employed individual continuum segments, improving the average repeatability by 67% for position and 167% for orientation, respectively.

In this letter, we study the so-called $\mathbf {p}$ -safety of a Markov chain. We say that a state is $\mathbf {p}$ -safe in a state space $S$ with respect to an unsafe set $U$ if the process stays in the state space and hits the set $U$ with the probability less than $\mathbf {p}$ . We show several ways of computing $\mathbf {p}$ -safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.

In this brief, we evaluate two techniques for obtaining mixed-radix digits using mixed-radix conversion technique, for the residue number system (RNS) moduli set $\{2^{n}-1, 2^{n}, 2^{n+1}-1\}$ . These are needed for comparison of two numbers in residue form, base extension to modulus $2^{n+e}$ and reverse conversion. The complete architectures are derived to estimate the hardware resource requirement and computation time for deriving the mixed-radix digits. The proposed techniques are also compared with designs based on other techniques available in literature. The trade-offs regarding hardware resource requirement, computation time and power dissipation are brought out.