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We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of each operator yields one cumulant. This direct relation offers a better numerical efficiency than the equivalent number-resolved master equation. The proposed method is particularly useful for conductors with an elaborate time-dependence stemming, e.g., from pulses or combinations of slow and fast parameter switching. As a test bench for the evaluation of the numerical stability, we consider time-independent problems for which the full-counting statistics can be computed by other means. As applications, we study cumulants of higher order for two time-dependent transport problems of recent interest, namely steady-state coherent transfer by adiabatic passage and Landau-Zener-St\"uckelberg-Majorana interference in an open double quantum dot., Comment: 7 pages, 5 figures

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing channels. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the order parameters and the trace of two-particle Green functions. In the presence of inversion symmetry, the superfluid density is directly related to the inverse of pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied into a multi-band fermion superfluid in lattice., Comment: 2 figures

By considering a weighted inner product, an adaptive generalized Arnoldi (GArnoldi) method was constructed by [ 13 ] for computing PageRank. In order to accelerate the adaptive GArnoldi method, this paper proposes a new method by using the power method with extrapolation process based on Google matrix's trace (PET) as an accelerated technique of the adaptive GArnoldi method. The new method is called as GArnoldi-PET method, whose implementation and convergence analysis are discussed in detail. Numerical experiments are used to illustrate the effectiveness of our proposed method.

Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carriers. We solve a practically relevant problem of finding an optimal initial encoding to distribute entangled polarized qubits through communication lines with polarization dependent losses and extra depolarizing noise. The longest entanglement lifetime is shown to be attainable with a state that is not maximally entangled.Quanta 2021; 10: 15–21.

Through the Loewner equation, real-valued driving functions generate sets called Loewner hulls. We analyze driving functions that approach 0 at least as fast as \(a (T-t)^r\) as \(t \to T\), where \(r \in (0, 1/2)\), and show that the corresponding Loewner hulls have tangential behavior at time \(T\). We also prove a result about trace existence and apply it to show that the Loewner hulls driven by \(a(T-t)^r\) for \(r \in (0,1/2)\) have a tangential trace curve.

In this paper, we study the modified gravity theory, where and represent the scalar-torsion and trace of energy-momentum tensor, respectively. According to our cosmological study, we show that the gravity theory has a good agreement with observations. Function type for can be determined by several factors. The most important motivation for determining is that the Lagrangian of model follows the Noether continues symmetry; therefore, according to the Noether approach, we try to determine the function of . Moreover, the proposed model should behave in agreement with observations in terms of phenomenology. As a result, we compared the predictions of the model with observation constrains, for example, the cosmic microwave background and Hubble diagram can be mentioned. In this paper, we study the gravity in the FRW space-time. So, we achieved the effective Lagrangian with respect to independent variables, scale factor , scalar-torsion and trace of energy-momentum tensor . After imposing the Noether symmetry to Lagrangian, we can introduce the suitable form for the function. . Then, we calculated the Noether conservative quantity for the model.

Aluminum (Al)-based metal-organic frameworks (MOFs) have been shown to have good stability toward γ irradiation, making them promising candidates for durable adsorbents for capturing volatile radioactive nuclides. In this work, we studied a series of existing Al-MOFs to capture trace radioactive organic iodide (ROI) from a gas composition (100 ppm CH3I, 400 ppm CO2, 21% O2, and 78% N2) resembling the off-gas composition from reprocessing the used nuclear fuel using Grand canonical Monte Carlo (GCMC) simulations and density functional theory (DFT) calculations. Based on the results and understanding established from studying the existing Al-MOFs, we proceed by functionalizing the top-performing CAU-11 with different functional groups to propose better MOFs for ROI capture. Our study suggests that extraordinary ROI adsorption and separation capability could be realized by -SO3H functionalization in CAU-11. It was mainly owing to the joint effect of the enhanced pore surface polarity arising from -SO3H functionalization and the μ-OH group of CAU-11.

We consider $U(N)$ $\mathcal N=4$ super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $\frac{1}{2}$-BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling $\lambda$, order by order in $1/N$, and then taking the $\lambda\gg 1$ limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885., Comment: 41 pages

Removal of trace SO2 from an SO2-containing product is now receiving increasing attention. However, designing a robust porous adsorbent with high SO2 adsorption capacity and good SO2/CO2 selectivity, as well as validity under humid conditions, is still a challenging task. Herein, we report a porous cage-based metal-organic framework, namely ECUT-111, which contains two distinct cages with apertures of 5.4 and 10.2 angstrom, respectively, and shows high a BET of up to 1493 m2/g and a pore volume of 0.629 cm3/g. Impressively, ECUT-111 enables an ultrahigh SO2 uptake of up to 11.56 mmol/g, exceeding most reported top-performing adsorbents for such a use. More importantly, complete separation of trace SO2 from SO2/CO2 and SO2/CO2/N2 mixtures, especially under humid conditions, and excellent recycle use were observed for ECUT-111, suggesting its superior application in desulfurization of SO2-containing products.

An effective and fairly inexpensive spectrophotometric method for tracing the determination of isoniazid (INH) in pure form, as well as in pharmaceutical formulations, has been developed through the ligand substitution reaction between INH and aquapentacyanoruthenate (II) ion ([Ru(CN)5OH2]3-) in aqueous medium at ?max = 502 nm. The fixed time procedure has been employed under optimum reaction conditions. The calibration equations, relating absorbance measured at 502 nm at fixed times (tn = 2, 5 and 7 min) and cINH in linear range 1.37-27.43 ?g mL-1, were used for the trace determination of INH, which has been reported in the present investigation and are in agreement with official and reported methods. The percentage recovery has been calculated and found to be within the range of 99?101 % in the analysis of different pharmaceutical samples. The results reveal that the use of common recipients as the used additives do not produce any type of interference in the suggested method. The validity of the proposed method was also checked by statistical analysis which agreed with the results obtained using the official method. The present method is very simple, reproducible, sensitive and it can be adopted for trace determination of INH in different samples without using extracting agent.

In the previous papers, it is pointed out that a supersymmetric double-well matrix model corresponds to a two-dimensional type IIA superstring theory on a Ramond-Ramond background at the level of correlation functions. This was confirmed by agreement between their planar correlation functions. The supersymmetry in the matrix model corresponds to the target space supersymmetry and it is shown to be spontaneously broken by nonperturbative effect. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all order of genus expansion in its double scaling limit. We found that this expansion is stringy and not Borel summable and hence there arises an ambiguity in applying the Borel resummation technique. We confirmed that resurgence works here, namely this ambiguity in perturbative series in a zero-instanton sector is exactly canceled by another ambiguity in a one-instanton sector obtained by instanton calculation. In this paper we extend this analysis and study resurgence structure of the two-point functions of the single trace operators. By using results in the random matrix theory, we derive two-point functions at arbitrary genus and see that the perturbative series in the zero-instanton sector again has an ambiguity. We find that the two-point functions inevitably have logarithmic singularity even at higher genus. In this derivation we obtain a new result of the two-point function expressed by the one-point function at the leading order in the soft-edge scaling limit of the random matrix theory. We also compute an ambiguity in the one-instanton sector by using the Airy kernel, and confirm that ambiguities in both sectors cancel each other at the leading order in the double scaling limit. We thus clarify resurgence structure of the two-point functions in the supersymmetric double-well matrix model., Comment: 50 pages, 4 figures, typos corrected

We compute the Hagedorn temperature of μT T ¯ $$ \mu T\overline{T} $$ + ε + J T ¯ $$ {\varepsilon}_{+}J\overline{T} $$ + ε − T J ¯ $$ {\varepsilon}_{-}T\overline{J} $$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of μ, ε +, and ε − for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed AdS 3 × S 1 × T 3 × S 3 using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on (μ, ε + , ε − ) of the double trace deformed compact scalars.

This paper presents an automated method for discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces. Specifically, the method consists of five steps: (1) detection of trace feature points by normal tensor voting theory, (2) contraction of trace feature points, (3) connection of trace feature points, (4) linearization of trace segments, and (5) connection of trace segments. A sensitivity analysis was then conducted to identify the optimal parameters of the proposed method. Three field cases, a natural rock mass outcrop and two excavated rock tunnel surfaces, were analyzed using the proposed method to evaluate its validity and efficiency. The results show that the proposed method is more efficient and accurate than the traditional trace mapping method, and the efficiency enhancement is more robust as the number of feature points increases.

The trace of the stress tensor characterizes the transformation of a theory under rescaling. In quantum chromodynamics (QCD), this trace contains contributions from the bare masses of the quarks and also from a purely quantum effect, called the QCD trace anomaly. It affects all masses in the theory. We present an estimation of the QCD trace anomaly from the near-threshold J/${\rm \Psi}$ photo-production data of the GlueX experiment, at JLab. We apply a vector meson dominance model to describe the photo-production of J/${\rm \Psi}$ and a running strong coupling which includes the nonperturbative effects in the low $\mu^2$ region. Despite the large uncertainty, we find that the experimental data favors a small value of the trace anomaly parameter $b=0.07\pm 0.17$. We report the resulting proton mass decompositions at $\mu^2=0.41$ GeV$^2$ and $\mu^2=4$ GeV$^2$., Comment: 6 pages, 4 figures

The influence of H2O on SF6 decomposition characteristics under positive DC partial discharge (PD) is significant. To evaluate PD fault severity in DC SF6-insulated equipment using the production characteristics of SF6 decomposition components, the corresponding relationship and mathematical expression between the production of SF6 decomposition components and the H2O content should be identified and achieved. Thus, SF6 decomposition experiments under positive DC PD are performed to reflect the influence of H2O on SF6 decomposition components. Results show that the total discharge quantity and the discharge repetition rate averaged for 1 s decrease slightly when the H2O content increases from 0 to 970 ppmv and then increase when the H2O content increases from 970 to 5120 ppmv. The effective production rates of SO2F2, SOF2, and SO2 increase with the H2O content, whereas that of SOF4 decreases. Finally, the corresponding relationship and mathematical expression between the characteristic ratio (c(SO2F2) + c(SOF4))/(c(SOF2) + c(SO2)) of components and the H2O content have been achieved, which can afford references for PD fault diagnosis in DC SF6 gas-insulated equipment.

Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work \cite{Hou:2018bwm}, we have already proven that the identities induced from tree level single-trace EYM amplitudes can be precisely expanded in terms of BCJ relations. In this paper, we extend the discussions to those identities induced from all tree level \emph{multi-trace} EYM amplitudes. Particularly, we establish a refined graphic rule for multi-trace EYM amplitudes and then show that the induced identities can be fully decomposed in terms of BCJ relations., Comment: 40 pages, 19 figures,typos corrected, sturecture is adjusted, more discussions are added, published in JHEP

In this work, static traversable wormholes are investigated in $$R^2$$R2 gravity with logarithmic trace term T, where R denotes the Ricci scalar, and $$T=-\rho +p_r+2p_t>0$$T=-ρ+pr+2pt>0, the trace of the energy momentum tensor. The connection between energy density of the matter component and the Ricci scalar is taken into account. Exact wormhole solutions are determined for three different novel forms of energy density: $$\rho =\alpha _1 R+\beta _1 R^{'}e^{\xi _1 R}$$ρ=α1R+β1R′eξ1R, $$\rho =\alpha _2 R e^{\xi _2 R}$$ρ=α2Reξ2R and $$\rho =\alpha _3 R^2+\beta _2 R^{'} e^{\xi _3 R^{'}}$$ρ=α3R2+β2R′eξ3R′, where prime denotes derivative with respect to r. The parameters $$\alpha _1$$α1, $$\beta _1$$β1, $$\xi _1$$ξ1, $$\alpha _2$$α2, $$\xi _2$$ξ2, $$\alpha _3$$α3, $$\xi _3$$ξ3 and $$\beta _2$$β2 play an important role for the absence of exotic matter inside the wormhole geometry. The parameter space is separated into numerous regions where the energy conditions are obeyed.

An H-infinity model predictive fault-tolerant control strategy is proposed for multi-phase batch processes with interval delay and actuator failures. First, state variables, state errors and output tracking errors are introduced to establish an extended-state-space switched system model. Then, based on this model, a predictive fault-tolerant control law is designed for tracking the set point by the output that satisfies the requirements of the optimal performance index under input and output constraints. The feasibility conditions for the solvability of the control law are presented in the form of linear matrix inequalities. In addition, the designed switching law is constructed, and the gain of the control law is obtained via the optimization algorithm. This design has several advantages: the output tracking is faster, the tracking performance is superior, and the trace is smoother at the switching time. Finally, through a comparison with traditional methods, the effectiveness and feasibility of this method are demonstrated via injection molding simulation.

The current runway width design in China was still according to the aircraft size and the accumulated experience in the flight process, and there is no clear calculation method. This paper proposed a new runway width design method based on the wheel traces distribution of the aircraft. A laser test system was developed to measure the aircraft wheel tracks of 17 cross sections along the runway at a feeder airport. The test results indicated that when aircraft takes off or lands, the transverse wheels traces obeyed a normal distribution. The variation curve in landing was selected to fit a numerical formula, which was used to calculate the maximum landing variation within the forward motion range, and the expression of the wheel trace transverse distribution on the section with the maximum discretization was determined. At last, a failure probability of 0.0001% was chosen as the criterion to determine the runway width. It was showed that B737-30 should have at least 45 m width to ensure the 0.0001 % failure probability.

International audience; This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case. The second is a formula for the multiplicities of generic representations in the $p$-adic case that extends previous work of Feigon-Lapid-Offen. Both results are stated in terms of Arthur-Clozel's quadratic local base-change and the proofs are based on local analogs of two relative trace formulas previously studied by Jacquet and Ye and known as (relative) Kuznetsov trace formulas.

In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order evolution equation which displays some challenging features. In the opening of his 1967 hypoellipticity paper Hörmander discussed a general class of degenerate Ornstein–Uhlenbeck operators that includes Kolmogorov’s as a special case. In this note we combine semigroup theory with a nonlocal calculus for these hypoelliptic operators to establish new inequalities of Hardy–Littlewood–Sobolev type in the situation when the drift matrix has nonnegative trace. Our work has been influenced by ideas of E. Stein and Varopoulos in the framework of symmetric semigroups. One of our objectives is to show that such ideas can be pushed to successfully handle the present degenerate non-symmetric setting.

The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$. We generalize this fact to the context of unrolled quantum groups and construct the associated topological ribbon Hopf algebras. Then we use such an algebra, the discrete Fourier transforms, a symmetrized graded integral and a modified trace to define a modified graded Hennings invariant. Finally, we use the notion of a modified integral to extend this invariant to empty manifolds and show that it recovers the CGP-invariant., 54 pages, 42 figures

The helical gear pairs are widely used in different mechanical constructs. The main advantage is the good efficiency and the low noise during the connection.We have worked out a computer software with which the designing process of the helical gears could be eased. Based on the calculated gear parameters the CAD models of the elements could be prepared. Knowing of the geometries the assembly could be created based on the fixed freedom degrees and the elementary centre distance. We have designed five types of gear pairs. The differences are only the different tooth traces. All of other parameters have not been modified. We have done TCA which is meant we have analyzed the effect of the modified parameter for the normal stress, normal deformation and the normal elastic strain on the contact zone. Based on the results we have prepared diagrams for the analysis of the correlations between the changing parameters.

We study the self-adjoint Dirac operators D = D0 + V (x), where D0 is the free three-dimensional Dirac operator and V (x) is a smooth compactly supported Hermitian matrix potential. We define resonances of D as poles of the meromorphic continuation of its cut-off resolvent. By analyzing the resolvent behaviour at the spectrum edges ±m, we establish a generalized Birman-Krein formula, taking into account possible resonances at ±m. As an application of the new Birman-Krein formula we establish the Poisson wave trace formula in its full generality. The Poisson wave trace formula links the resonances with the trace of the difference of the wave groups. The Poisson wave trace formula, in conjunction with asymptotics of the scattering phase, allows us to prove that, under certain natural assumptions on V , the perturbed Dirac operator has infinitely many resonances; a result similar in nature to Melrose’s classic 1995 result for Schr¨odinger operators.

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the $GW$ approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot $GW$ method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard $GW$ approximation and find, in particular, that i) some neutral excitation energies become complex when the electron-electron interaction $U$ increases, which can be traced back to the approximate nature of the $GW$ quasiparticle energies; ii) the BSE formalism yields accurate correlation energies over a wide range of $U$ when the trace (or plasmon) formula is employed; iii) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); iv) the trace formula has the correct behavior for weak (\ie, small $U$) interaction, unlike the ACFDT expression., Comment: 12 pages, 4 figures

Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.

The exponential form of the original Phan-Thien and Tanner (PTT) model is often used to study complex viscoelastic fluids. Recently, a generalised version of the PTT model, that uses the Mittag-Leffler function to compute a new function of the trace of the stress tensor, was proposed. This new model adds one or two additional fitting parameters that allow for greater fitting capability. In this paper, we propose two optimisation problems for estimating the model parameters when fitting experimental data in shear (storage modulus, loss modulus, shear viscosity). We also propose a numerical sequential approach for solving one of these problems. The optimal values for the parameters produced by the optimisation approach allow the model to reproduce almost exactly the experimental data., Supported by FCT -Fundacao para a Ciencia e a Tecnologia, through projects UIDB/00013/2020 and UIDP/00013/2020, and CMAT -Centre of Mathematics, University of Minho.

We compute trace anomaly contribution to hydrogen atom mass, which turns out to be related to the part of the Lamb shift. This finding might shed new light on our understandings of the mass structure of QCD bound states, such as, proton., Comment: 8 pages, 3 figures

Knot matrix models are defined so that the averages of characters are equal to knot polynomials. From this definition one can extract single trace averages and generation functions for them in the group rank – which generalize the celebrated Harer-Zagier formulas for Hermitian matrix model. We describe the outcome of this program for HOMFLY-PT polynomials of various knots. In particular, we claim that the Harer-Zagier formulas for torus knots factorize nicely, but this does not happen for other knots. This fact is mysteriously parallel to existence of explicit β=1 eigenvalue model construction for torus knots only, and can be responsible for problems with construction of a similar model for other knots.

We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of ${\cal N}=2$ SQCD on $S^4$, to all orders in the 't Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ${\mathbb R}^4$. Specifically, we compute all the terms with a single value of the $\zeta$ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ${\mathbb R}^4$., Comment: 25 pages. v2 : added reference

We obtain a trace Hardy inequality for the Euclidean space with a bounded cut Σ ⊂ R d , d ≥ 2 . In this novel geometric setting, the Hardy-type inequality non-typically holds also for d = 2 . The respective Hardy weight is given in terms of the geodesic distance to the boundary of Σ. We provide its applications to the heat equation on R d with an insulating cut at Σ and to the Schrodinger operator with a δ ′ -interaction supported on Σ. We also obtain generalizations of this trace Hardy inequality for a class of unbounded cuts.

This paper deduces exponential matrix concentration from a Poincare inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincare inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument.

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach., 30 pages, to be published in "Symmatry: Manifest and Hidden Symmetries in Field and String Theories"

We study hard $1\to 2$ final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an effect that is encapsulated in a Wilson line along their trajectory. When calculating observables, one typically has to calculate traces of two or more medium-averaged Wilson lines. These are usually dealt with in the literature by invoking the large-$N_c$ limit, but exact calculations have been lacking in many cases. In our work, we show how correlators of multiple Wilson lines appear, and develop a method to calculate them numerically to all orders in $N_c$. Initially, we focus on the trace of four Wilson lines, which we develop a differential equation for. We will then generalize this calculation to a product of an arbitrary number of Wilson lines, and show how to do the exact calculation numerically, and even analytically in the large-$N_c$ limit. Color sub-leading corrections, that are suppressed with a factor $N_c^{-2}$ relative to the leading scaling, are calculated explicitly for the four-point correlator and we discuss how to extend this method to the general case. These results are relevant for high-$p_T$ jet processes and initial stage physics at the LHC., 39 pages, 8 figures

Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite operators of low dimension, then do this with traceless tensor operators. We then express the bare energy momentum tensor in terms of the renormalised composite operators, with some terms having divergent coefficients. We subtract these away and obtain a manifestly finite energy tensor. The subtracted terms are transverse, so this does not affect the conservation of the energy momentum tensor. The trace of this finite improved energy momentum tensor vanishes at the fixed point indicating conformal invariance. Interestingly it is not RG-invariant except at the fixed point, but can be made RG invariant everywhere by further addition of transverse terms, whose coefficients vanish at the fixed point., Comment: v2: added arxiv numbers for references, added page numbers, added email id, and corrected one typo in eqn in page 15. v1: 32 pages, 5 figures

In this work, we have adopted gravitational decoupling by Minimal Geometric Deformation (MGD) approach and have developed an anisotropic version of well-known Tolman VII isotropic solution in the framework of $f(R, T)$ gravity, where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor. The set of field equations has been developed with respect to total energy momentum tensor, which combines effective energy momentum tensor in $f(R,T)$ gravity and additional source $\phi_{ij}$. Following MGD approach, the set of field equations has been separated into two sections. One section represents $f(R, T)$ field equations, while the other is related to the source $\phi_{ij}$. The matching conditions for inner and outer geometry have also been discussed and an anisotropic solution has been developed using mimic constraint for radial pressure. In order to check viability of the solution, we have considered observation data of three different compact star models, named PSR J1614-2230, PSR 1937+21 and SAX J1808.4-3658 and have discussed thermodynamical properties analytically and graphically. The energy conditions are found to be satisfied for the three compact stars. The stability analysis has been presented through causality condition and Herrera's cracking concept, which ensures physical acceptability of the solution., Comment: 14 pages, 04 figures

We study the impact of deviations from the Kennicutt-Schmidt relation (quantified by the `burstiness' parameter $\kappa_s$), gas metallicity ($Z$), and density ($n$) on the observed [OIII]88$\mu$m/[CII]158$\mu$m surface brightness ratios ($\Sigma_{[OIII]}/\Sigma_{[CII]}$) in nine galaxies at $z\approx6-9$. We first discuss possible biases in the measured $\Sigma_{[OIII]}/\Sigma_{[CII]}$ ratios by comparing the data with zoom-in cosmological simulations, and then use a Markov Chain Monte Carlo algorithm to derive the best fit values of ($\kappa_s, Z, n$). We find that (i) the strongest dependence of $\Sigma_{[OIII]}/\Sigma_{[CII]}$ is on $\kappa_s$; (ii) high ratios identify starburst galaxies with short gas depletion times ($t_{dep}=6-49\,\rm Myr$); (iii) a secondary dependence on density is found, with $\Sigma_{[OIII]}/\Sigma_{[CII]}$ anticorrelating with $n$ as a result of the lower [OIII] critical density, (iv) the ratio only weakly depends on $Z$. The nine galaxies are significantly enriched (Z=0.2-0.5 $Z_\odot$), and dense ($n=10^{1-3} {\rm cm}^{-3}$). This lends further support to the starburst scenario in which a rapid enrichment of the interstellar medium is expected., Comment: accepted for publication in MNRAS, 12 pages, 8 figures

We prove some local estimates on the trace of spectral projectors for random Schrodinger operators restricted to cubes \(\Lambda \subset \mathbb {R}^d\). We also present a new proof of the spectral averaging result based on analytic perturbation theory. Together, these provide another proof of the Wegner estimate with an explicit form of the constant and an alternate proof of the Birman-Solomyak formula. We also use these results to prove the Lipschitz continuity of the local density of states function for a restricted family of random Schrodinger operators on cubes \(\Lambda \subset \mathbb {R}^d\), for \(d \geqslant 1\). The result holds for low energies without a localization assumption but is not strong enough to extend to the infinite-volume limit.

This article focuses on the relationships between major (Si, Al, Mg, Fe, Ca, Na, K, S, P and Ti) and potentially toxic trace (Ag, As, B, Ba, Bi, Co, Cd, Cr, Cu, F, Ge, Mo, Mn, Li, Ni, Pb, Sb, Sn, Sr, Tl, V and Zn) elements in Ulaanbaatar surface soils and also sources of the trace elements in the soils distinguished by the methods of multivariate statistical analysis. Results of exploratory data analysis of 325 Ulaanbaatar soil samples show the accumulation of Ca, S, B, Bi, Cu, Mo, Pb, Sb, Sn, Sr and Zn in urban soils. The major elements were grouped by cluster analysis in tree associations characterizing main soil fractions: sandy P-(K-Na-Si), clayey (Mg-Ti-Fe-Al) and silty (S-Ca). The factor analysis shows that silty fraction is enriched in major elements of both natural and anthropogenic origin. The principal component analysis from 32 variables extracted nine principal components with 82.49% of the cumulative explained variance. The results of cluster and factor analyses well agree and reaffirm the enrichment causes of potentially toxic elements are a coal combustion at thermal power stations (B, Bi, Ca, Mo, S and Sr) and traffic emissions (Cu, Pb, Sn and Zn). Spatial distributions of trace elements in the districts of Ulaanbaatar city were obtained by ordinary kriging. It is illustrated that the different principal components define the various origins and patterns of accumulation of trace elements in soils. The supplementation of data set by the concentration of organic carbon and the species of elements could help to identify the sources of such elements as P, Ni, Al, Fe, Ca, Ba, Bi, Cr, Zn, Sr and Sb in urban soils more completely.

The $f(R,T)$ gravity field equations depend generically on both the Ricci scalar $R$ and trace of the energy-momentum tensor $T$. Within the assumption of perfect fluids, the theory carries an arbitrariness regarding the choice of the matter lagrangian density $\mathcal{L}$, not uniquely defined. Such an arbitrariness can be evaded by working with the trace of the theory field equations. From such an equation, one can obtain a form for $\mathcal{L}$, which does not carry the arbitrariness. The obtained form for $\mathcal{L}$ shows that the $f(R,T)$ gravity is unimodular. A new version of the theory is, therefore, presented and forthcoming applications are expected., 5 pages

The objective of the study was to investigate a new notion of generalized trace pseudo-spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra. RESUMEN El objetivo de este estudio es investigar una nueva noción de pseudo-espectro traza generalizado para pinceles de matrices. En particular, demostramos variadas propiedades nuevas e interesantes del pseudo-espectro traza generalizado. Adicionalmente, mostramos un análogo del teorema espectral de aplicaciones para el pseudo-espectro traza generalizado en el álgebra de matrices.

We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed., 20 pages

A parabolic equation related to the p-Laplacian is considered. If the equation is degenerate on the boundary, then demonstrating the regularity on the boundary is difficult, the trace on the boundary cannot be defined, in general. The existence and uniqueness of weak solutions are researched. Based on uniqueness, the stability of solutions can be proved without any boundary condition.

It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical description of gravity proposed by Regge and Teitelboim, treating it also as general relativity with some additional matter. We propose a form of action which allows to describe this matter in terms of conserved currents. This action turns out to be a generalization of the perfect fluid action, which can be useful in the analysis of the properties of the additional matter. On the other side, the action contains a trace of the root of the matrix product, which is similar to the constructions appearing in bimetric theories of gravity. The action is completely equivalent to the original embedding theory, so it is not just some artificial model, but has a clear geometric sense. We discuss the possible equivalent forms of the theory and ways of study of the appearing equations of motion., LaTeX, 11 pages

The structure of bonds in biomolecules, such as base pairs in RNA chains or native interactions in proteins, can be presented in the form of a chord diagram. A given biomolecule is then characterized by the genus of an auxiliary two-dimensional surface associated to such a diagram. In this work we introduce the notion of the genus trace, which describes dependence of genus on the choice of a subchain of a given backbone chain. We find that the genus trace encodes interesting physical and biological information about a given biomolecule and its three dimensional structural complexity; in particular it gives a way to quantify how much more complicated a biomolecule is than its nested secondary structure alone would indicate. We illustrate this statement in many examples, involving both RNA and protein chains. First, we conduct a survey of all published RNA structures with better than 3 Å resolution in the PDB database, and find that the genus of natural structural RNAs has roughly linear dependence on their length. Then, we show that the genus trace captures properties of various types of base pairs in RNA, and enables the identification of the domain structure of a ribosome. Furthermore, we find that not only does the genus trace detect a domain structure, but it also predicts a cooperative folding pattern in multi-domain proteins. The genus trace turns out to be a useful and versatile tool, with many potential applications.

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes., This research was partially supported by FCT (Fundacao para a Ciencia e a Tecnologia, Portugal) through project UID/MAT/00013/2013.

Ultralong room temperature phosphorescence could be generated after adding trace-specific ingredients into organic compounds., Pure organic persistent room temperature phosphorescence (RTP) has shown great potential in information encryption, optoelectronic devices, and bio-applications. However, trace impurities are generated in synthesis, causing unpredictable effects on the luminescence properties. Here, an impurity is isolated from a pure organic RTP system and structurally characterized that caused an unusual ultralong RTP in matrix even at 0.01 mole percent content. Inspired by this effect, a series of compounds are screened out to form the bicomponent RTP system by the trace ingredient incorporation method. The RTP quantum yields reach as high as 74.2%, and the lifetimes reach up to 430 ms. Flexible application of trace ingredients to construct RTP materials has become an eye-catching strategy with high efficiency, economy, and potential for applications as well as easy preparation.

The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions. The trace and Weyl anomalies are then employed to probe the MGD in the holographic setup, as a realistic model, playing a prominent role in AdS/CFT., Comment: 8 pages

We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region., 49 pages, 3 figures

We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as $N \to \infty$, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings., 81 pages, 23 figures. V2: added short discussion on the modified dip time, and corrected minor typos