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We propose an efficient version of ensemble Hartree–Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions—even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future. [ABSTRACT FROM AUTHOR]

We present an exchange–correlation approximation in which the Coulomb interaction is split into long- and short-range components and the range separation is determined by a non-empirical density functional. The functional respects important constraints, such as the homogeneous and slowly varying density limits, leads to the correct long-range potential, and eliminates one-electron self-interaction. Our approach is designed for spectroscopic purposes and closely approximates the piecewise linearity of the energy as a function of the particle number. The functional's accuracy for predicting the fundamental gap in generalized Kohn–Sham theory is demonstrated for a large number of systems, including organic semiconductors with a notoriously difficult electronic structure. [ABSTRACT FROM AUTHOR]

The observed metastable characteristics of cation vacancies in Ga2O3 have prompted a wider search for such systems. In this Perspective, we consider a number of defect systems as candidates for metastability. Some of these are already known to have this property, while for others, this suggestion is new. The examples discussed here are but a sampling of a huge number of systems, and these are used to emphasize that the metastability of defect structures is both common and important; it may yield (for example) split vacancy equilibrium configurations and, hence, should be considered in developing defect models and in analyzing their properties. [ABSTRACT FROM AUTHOR]

We present a Wave Operator Minimization (WOM) method for calculating the Fermi–Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods. [ABSTRACT FROM AUTHOR]

We investigate the magnetization and the Dzyaloshinskii–Moriya interactions (DMI) in Pt/Co/Re thin films in the case of perfect interfaces and upon the introduction of intermixing on both Co interfaces. Calculations were implemented on a series of systems with a countable number of cobalt atomic layers. Remarkably, Re can introduce a DMI at the interface with cobalt and also increase the DMI at the Pt/Co interface. We demonstrate that the chiral magnetic multilayer Pt/Co/Re with a chiral spin structure can achieve a substantial DMI value, which is almost double that attained in the prototype system Pt/Co/W. We also study the DMI as a function of the Re thickness, finding the optimal thickness to maximize the DMI. When we include a disorder that cancels a contribution from all first-neighbor Co atoms in the intermixed region, we find out that intermixing at the two interfaces affects the strength of the DMI solely when introduced at the Pt/Co interface, where the DMI loses almost half of its value. On the contrary, the mixing at the Co/Re interface has very little or no effect where the calculated values were not significantly decreased as compared to the case with perfect interfaces. [ABSTRACT FROM AUTHOR]

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis–Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis–Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population. [ABSTRACT FROM AUTHOR]

The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may not be paramount in explicit dynamics, a substantial reduction in the critical time step size based on the smallest volume fraction χ of a cut element is observed. This reduction can be so drastic that it renders explicit time integration schemes impractical. To tackle this challenge, we propose the use of a dedicated eigenvalue stabilization (EVS) technique. The EVS-technique serves a dual purpose. Beyond merely improving the condition number of system matrices, it plays a pivotal role in extending the critical time increment, effectively broadening the stability region in explicit dynamics. As a result, our approach enables robust and efficient analyses of high-frequency transient problems using immersed boundary methods. A key advantage of the stabilization method lies in the fact that only element-level operations are required. This is accomplished by computing all eigenvalues of the element matrices and subsequently introducing a stabilization term that mitigates the adverse effects of cutting. Notably, the stabilization of the mass matrix M c of cut elements – especially for high polynomial orders p of the shape functions – leads to a significant raise in the critical time step size Δ t cr. To demonstrate the efficiency of our technique, we present two specifically selected dynamic benchmark examples related to wave propagation analysis, where an explicit time integration scheme must be employed to leverage the increase in the critical time step size. [ABSTRACT FROM AUTHOR]

The present study investigates the impact of a magnetic field on double‐diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge‐Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for Le<1 $Le\lt 1$, the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of Le=1 $Le=1$, the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non‐monotonic for traveling rolls. Moreover, for Le>1 $Le\gt 1$, the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non‐monotonic behavior. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a multiphase digital control called digital integration constant on‐time (DICOT) control is proposed, which applies the concept of signal accumulation, solves the drawbacks of ripple‐based digital COT control that the switching frequency and transient performance are affected by the A/D sample delay and sampling noise. Besides, the multiphase interleaving approach of the proposed DICOT control is well‐suitable for digital control and no higher calculation frequency is required compared to single‐phase. In the aspect of the current balance, almost all existing researches work on analog COT current balance scheme and few works are investigating the resolution improvement of digital COT current balance. In this paper, the current balance model of multiphase COT control is derived and can be applied in the Buck system with an arbitrary number of phases, the delay‐line‐based high‐resolution COT current balance scheme is proposed to enhance the control resolution. Finally, the two‐phase DICOT control is tested on the multiphase Buck system, the transient performance is tested of 100 A load step with the slew rate of 1000 A/μs, and the voltage undershoot and overshoot are 20 and 36 mV, respectively. The current balance is tested and the errors are 0.01% and 0.11% at the light and heavy loads, respectively. [ABSTRACT FROM AUTHOR]

Understanding satellite system-specific artifacts and geophysical phenomena affecting coordinate estimates using multi-Global Navigation Satellite System (GNSS) data is of vital importance to ensure the accuracy and reliability of positioning, enabling scientific research to yield trustworthy and informed results. Therefore, this study is conducted to investigate the precision of single/multi-system solutions, factors affecting these precisions due to spurious periodic signals, and the mitigation of these signal powers in the frequency domain after fusing multi-GNSS data. For this purpose, the multi-GNSS data from 46 globally distributed International GNSS Service (IGS) stations spanning from January 1st, 2020 to August 31st, 2022, were processed using PRIDE-PPPAR v2.2 software in Precise Point Positioning (PPP) mode for GPS-, GLONASS-, Galileo-, and BeiDou-only solutions, as well as all possible combinations with GPS. The coordinates in the time domain were then converted into the frequency domain utilizing the Lomb-Scargle algorithm. The results of this experiment indicated that the GPS-only solutions have the best coordinate precision among the other satellite systems. The GLONASS, Galileo, and BeiDou systems exhibit orbital resonance up to the 3rd, 4th, and 3rd harmonics, respectively, whereas the GPS system, with a half of a sidereal day orbital period, exhibits no resonant effects due to the Nyquist frequency in the daily sampled time series. Enhanced coordinate precision for the multi-GNSS solutions was achieved with the GPS + GLONASS + Galileo + BeiDou combination (with only 0.1 mm deterioration in the east component), as well as the GPS + GLONASS + Galileo and GPS + Galileo combinations. The power spectra, particularly for the quadruple multi-GNSS combination, revealed that the system-specific periodic signals for GLONASS, Galileo, and BeiDou lost, on average, 85%, 55%, and 75% of their power in all components, respectively. Omitting the BeiDou and GLONASS systems from the quadruple and triple combinations slightly altered the power reductions of the Galileo systems. In other words, power reductions for orbital artifacts decreased as the number of satellite systems in the combination decreased. Interestingly, omitting specific systems did not significantly affect the fortnightly signals in multi-GNSS solutions. [ABSTRACT FROM AUTHOR]

We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence of integer bases and the Rényi system with one real base. We focus on the case of an alternate base B given by a purely periodic sequence (β n) n ≥ 1 of real numbers greater than 1. We answer an open question of Charlier et al. (J Number Theory 254:184–198, 2024, https://doi.org/10.1016/j.jnt.2023.07.008) on the set of numbers with eventually periodic B -expansions. We also investigate for which bases all sufficiently small rationals have a purely periodic B -expansion. We show that a necessary condition for this phenomenon is that δ = ∏ n = 1 p β n (where p is the period-length of B ) is a Pisot or a Salem unit. We also provide a sufficient condition. We thus generalize the results known for the Rényi numeration system, i.e. for the case when p = 1 . We provide a class of alternate bases in which all rational numbers in the interval [0, 1) have a purely periodic B -expansion. [ABSTRACT FROM AUTHOR]

Light microscopy facilities vary in the number of imaging systems and the scope of technologies they support. Each facility must craft an identity through the selection of equipment and development of staff in order to serve the needs of its local research environment. The process of crafting a light microscopy facility can be compared to curation of an art exhibition: great care should be given to the selection and placement of each object in order to make a coherent statement. Lay Description: Light microscopy facilities vary in the number of imaging systems and the scope of technologies they support. Each facility must develop an identity through the selection of equipment and development of staff in order to serve the needs of its local research environment. The process of crafting a light microscopy facility can be compared to curation of an art exhibition: great care should be given to the selection and placement of each object in order to make a coherent statement. [ABSTRACT FROM AUTHOR]

Fog computing provides a suitable development for real-time processing in the Internet of Things (IoT). Attribute-based encryption (ABE) is the main method to control data access in fog computing. A residue number system (RNS) can speed up multiplication and exponential operations by converting very large integers to small integers. This paper proposes a fine-grained lightweight access control scheme using ABE modified with RNS properties (RNS-ABE) with fog computing. Decryption is implemented with the Chinese remainder theorem (CRT), and a new access structure based on the CRT secret sharing scheme is also introduced. Security of the proposed scheme proved based on RNS properties and the complicated problem of factoring a very large integer into its large prime factors, like RSA encryption. The time cost comparison shows that the total encryption and decryption time of our scheme is more efficient than the lightweight schemes with the underlying operation of bilinear pairing. [ABSTRACT FROM AUTHOR]

Patient positioning interacts with a number of body systems and can impact clinically important perioperative outcomes. In this educational review, we present the available evidence on the impact that patient positioning can have in the pediatric perioperative setting. A literature search was conducted using search terms that focused on pediatric perioperative outcomes prioritized by contemporary research in this area. Several key themes were identified: the effects of positioning on respiratory outcomes, cardiovascular outcomes, enteral function, patient and carer‐centered outcomes, and soft issue injuries. We encountered considerable heterogeneity in research in this area. There may be a role for lateral positioning to reduce respiratory adverse outcomes, head elevation for intubation and improved oxygenation, and upright positioning to reduce peri‐procedural anxiety. [ABSTRACT FROM AUTHOR]

Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobounded hyperbolic actions of many abelian‐by‐cyclic groups associated to expanding integer matrices. Each such action is equivalent to an action on a tree or on a Heintze group (a classically studied class of negatively curved Lie groups). Our investigations incorporate number systems, factorization in formal power series rings, completions, and valuations. [ABSTRACT FROM AUTHOR]

Mass transfer technology for large quantities of tiny substances, such as electronic chips and drug particles, plays a crucial role in many industries. This study proposes a transferring system for large quantities of small objects based on the synergism of triboelectric nanogenerators (TENGs) and photo‐responsive dielectric materials. TENG device can provide an output voltage of over 8 kV within a rotation time of 40 ms and the titanium oxide phthalocyanine (TiOPc) photoconductive films are fabricated as the photo‐responsive interface, in order to match the output impedance of TENG. The transfer system enables a maximum adsorption load of 98 mg mm−2, which is enough for handling all common electronics chips/wafers. Under the stimulation of laser light, the conductivity of the TiOPc interface can be increased by two orders of magnitude within 1 ms, which leads to the vanish of the surface potential on the laser spot and the release of patterned or pointed object. This photo‐responsive strategy can achieve both large quantity transfer of tiny objects and highly selective release of the element at designed position. This collaborative mechanism of electrostatic force and photoconductivity provides a different approach for realizing efficient and precise Mass transfer system of semiconductor and chip industry. [ABSTRACT FROM AUTHOR]

In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem. [ABSTRACT FROM AUTHOR]

We propose a balanced $ 5 $ 5-moduli set $ P = \{{{2^q}, {2^q} - 1,{2^{q + 1}} - 1,{2^{q + 1}} + 1,{2^{q + 2}} - 1} \} $ P={2q,2q−1,2q+1−1,2q+1+1,2q+2−1}, for odd $ q \ge 3 $ q≥3. Our reverse conversion scheme is based on a multi-stage new Chinese remainder theorem, where some of the difficult-to-derive multiplicative inverse coefficients are expressed as geometric series. Only carry-save and ripple-carry adders are used as components of the corresponding circuits. Analytical gate-level evaluations are performed on the proposed and reference converters, whose results are confirmed by the synthesis tool. A comparison of the converters for moduli sets with equal dynamic range shows that $ P $ P is similar to previous 5-moduli set $ \{{{2^q}, {2^q} - 1,{2^q} + 1,{2^{q + 1}} - 1,{2^{q - 1}} - 1} \} $ {2q,2q−1,2q+1,2q+1−1,2q−1−1} and shows slight advantage in delay and energy consumption. [ABSTRACT FROM AUTHOR]

The present study considers a single-server Markovian queueing system by observing the number of customer arrivals during the service time of a customer. We estimate the traffic intensity in this queueing system along with the average queue length and the expected number of customers in the system. We propose classical and Bayesian frameworks to estimate the parameters of interest. In the Bayesian setup, three forms of prior distributions for ρ and two loss functions are considered. Furthermore, the predictive distribution of the number of customer arrivals during the service time of a customer and the equal-tailed credible region of ρ are obtained. The aforementioned approaches are illustrated with numerical examples based on simulation studies. [ABSTRACT FROM AUTHOR]

The onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the "weighted residual method." The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we define a mixed-base number system over a Weyl group Dn, the group of even-signed permutations. We introduce one-to-one correspondence between the positive integers of the set {1, · · ·, 2n-1n!} and elements of this group, after constructing the subexceedant function associated with the group. Thus, the integer representations of all the classical Weyl groups are now completed. Furthermore, we present an inversion statistic on the group Dn by using a decomposition of a positive root system of this reflection group. This inversion statistic is compatible with the length function on the group Dn. Then we derive some combinatorial properties for the inversion statistic. In addition, we prove that the D-major index is equi-distributed with this inversion statistic on Dn. Finally, we propose a public-key cryptosystem based on both the generalized hidden discrete logarithm problem and the integer representation over the group Dn. [ABSTRACT FROM AUTHOR]

We describe a Kolyvagin system-theoretic refinement of Gross–Zagier formula by comparing Heegner point Kolyvagin systems with Kurihara numbers when the root number of a rational elliptic curve E over an imaginary quadratic field K is -1. When the root number of E over K is 1, we first establish the structure theorem of the p^\infty-Selmer group of E over K. The description is given by the values of certain families of quaternionic automorphic forms, which is a part of bipartite Euler systems. By comparing bipartite Euler systems with Kurihara numbers, we also obtain an analogous refinement of Waldspurger formula. No low analytic rank assumption is imposed in both refinements. We also prove the equivalence between the non-triviality of various "Kolyvagin systems" and the corresponding main conjecture localized at the augmentation ideal. As consequences, we obtain new applications of (weaker versions of) the Heegner point main conjecture and the anticyclotomic main conjecture to the structure of p^\infty-Selmer groups of elliptic curves of arbitrary rank. In particular, the Heegner point main conjecture localized at the augmentation ideal implies the strong rank one p-converse to the theorem of Gross–Zagier and Kolyvagin. [ABSTRACT FROM AUTHOR]

Quaternions are a non-commutative associative number system that extends complex numbers, first described by Hamilton in 1843. We present algorithms for solving the eigenvalue problem for arrowhead and DPRk (diagonal-plus-rank-k) matrices of quaternions. The algorithms use the Rayleigh Quotient Iteration with double shifts (RQIds), Wielandt's deflation technique and the fact that each eigenvector can be computed in O (n) operations. The algorithms require O (n 2) floating-point operations, n being the order of the matrix. The algorithms are backward stable in the standard sense and compare well to the standard QR method in terms of speed and accuracy. The algorithms are elegantly implemented in Julia, using its polymorphism feature. [ABSTRACT FROM AUTHOR]

The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially in terms of approximating the invariant distribution. The triangle inequality framework employed in this paper is a convenient approach to estimate the long-time sampling error of the numerical methods. Using the triangle inequality framework, we show that the long-time error of the discrete random batch method is |$O(\sqrt {\tau } + e^{-\lambda t})$|⁠ , where |$\tau $| is the time step and |$\lambda $| is the convergence rate, which does not depend on the time step |$\tau $| or the number of particles |$N$|⁠. Our results also apply to the McKean–Vlasov process, which is the mean-field limit of the interacting particle system as the number of particles |$N\rightarrow \infty $|⁠. [ABSTRACT FROM AUTHOR]

The Neutrosophic Numeral System Algorithms are a set of techniques designed to handle uncertainty and ambiguity in numerical data. These algorithms use Neutrosophic Set Theory, a mathematical framework that deals with incomplete, indeterminate, and inconsistent information. In this paper, we provide an overview of different approaches used in Neutrosophic Numeral System Algorithms, including Neutrosophic Binary System, Neutrosophic Decimal System, and Neutrosophic Octal System. These systems use different bases and representations to account for degrees of truth, indeterminacy, and falsity in numerical data. We also explore the relationship between Neutrosophic Numeral System Algorithms and Number Neutrosophic Systems, which are another type of Neutrosophic System used for representing numerical data. Number Neutrosophic Systems use Neutrosophic Numbers to represent degrees of truth, indeterminacy, and falsity in numerical data, and they can be used in conjunction with Neutrosophic Numeral System Algorithms to handle uncertainty and ambiguity in decision-making and artificial intelligence applications. Moreover. We discuss the advantages and disadvantages of each algorithm and their potential applications in various fields. Finally, we highlight the importance of Neutrosophic cryptography in addressing uncertainty and ambiguity in decision making and artificial intelligence and discuss future research directions. Understanding Neutrosophic Numeral System Algorithms and their relationship with Number Neutrosophic Systems is crucial for developing effective techniques for handling uncertainty and ambiguity in numerical data in decision-making, pattern recognition, and artificial intelligence applications. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce generalized quaternions with hyper-number coefficients. For this, firstly, a new number system is defined, which is the generalization of bicomplex numbers, hyper-double numbers and hyper-dual numbers. And any element of this generalization is called a hyper-number. Then, real matrix representation and vector representation of a hyper-number are given. Secondly, hyper-number generalized quaternions and their algebraic properties are introduced. For a hyper-number generalized quaternion, real generalized quaternion matrix representation is presented. Next, because of lack of commutativity, for a hyper-number generalized quaternion, two different hyper-number matrix representations are calculated. Moreover, real matrix representations of a hyper-number generalized quaternion is expressed by matrix representation of a hyper-number. Finally, vector representations of a hyper-number generalized quaternion are given and properties of this representations are investigated. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light–matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems. [ABSTRACT FROM AUTHOR]

In the current work, we study the eigenvalue distribution results of a class of non-normal matrix-sequences which may be viewed as a low rank perturbation, depending on a parameter β > 1 , of the basic Toeplitz matrix-sequence { T n (e i θ) } n ∈ N , i 2 = − 1. The latter of which has obviously all eigenvalues equal to zero for any matrix order n , while for the matrix-sequence under consideration we will show a strong clustering on the complex unit circle. A detailed discussion on the outliers is also provided. The problem appears mathematically innocent, but it is indeed quite challenging since all the classical machinery for deducing the eigenvalue clustering does not cover the considered case. In the derivations, we resort to a trick used for the spectral analysis of the Google matrix plus several tools from complex analysis. We only mention that the problem is not an academic curiosity and in fact stems from problems in dynamical systems and number theory. Additionally, we also provide numerical experiments in high precision, a distribution analysis in the Weyl sense concerning both eigenvalues and singular values is given, and more results are sketched for the limit case of β = 1. [ABSTRACT FROM AUTHOR]

In this paper, we give characterization of quadratic ε -canonical number system (ε −CNS) polynomials for all values ε ∈ [ 0 , 1). Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials (ε = 0) and quadratic SCNS polynomials (ε = 1 / 2). This result is a consequence of our new characterization results of ε -shift radix systems (ε −SRS) in the two-dimensional case and their relation to quadratic ε −CNS polynomials. [ABSTRACT FROM AUTHOR]

In this article, we consider parabolic partial differential equations in (2+1) dimensions, with a focus on optimal convergence for solutions that are smooth in time but have corner singularities in space owing to the non-smoothness of the spatial boundary. The method employs geometric mesh along with a nonconforming least squares spectral element approximation in space coupled with the implicit Crank-Nicolson finite difference scheme in time. The unconditional stability of the scheme is rigorously proved and the error estimate which is almost optimal second order accurate in time and exponentially accurate in space is established. At each time instant, the subdivided problem is solved in parallel via the preconditioned conjugate gradient method in different processors by using an almost optimal preconditioner, in the sense that the condition number of the resulting system is O ((l n N) 2) (N being the degree of spatial approximation), without having to store any stiffness (or mass) matrix or load vector and the inter-element communication is established through Message Passing Interface (MPI). Specific numerical examples are presented with regard to the performance of the scheme. [ABSTRACT FROM AUTHOR]

The search for exomoons in time-domain photometric data has to-date generally consisted of fitting transit models that are comprised of a planet hosting a single moon. This simple model has its advantages, but it may not be particularly representative, as most of the major moons in our Solar system are found in multimoon satellite systems. It is critical that we investigate, then, the impact of applying a single-moon model to systems containing multiple moons, as there is the possibility that utilizing an inaccurate or incomplete model could lead to erroneous conclusions about the system. To that end, in this work we produce a variety of realistic multimoon light curves, perform standard single-moon model selection, and analyse the impacts that this model choice may have on the search for exomoons. We find that the number of moons in a system fit with a single-moon model generally has little impact on whether we find evidence for a moon in that system, and other system attributes are individually not especially predictive. However, the model parameter solutions for the moon frequently do not match any real moon in the system, instead painting a picture of a 'phantom' moon. We find no evidence that multimoon systems yield corresponding multimodal posteriors. We also find a systematic tendency to overestimate planetary impact parameter and eccentricity, to derive unphysical moon densities, and to infer potentially unphysical limb darkening coefficients. These results will be important to keep in mind in future exomoon search programmes. [ABSTRACT FROM AUTHOR]

Studies have demonstrated a significant correlation between the approximate number system (ANS) and early mathematical achievement. However, various explanations exist regarding the underlying cognitive mechanisms that underpin this association. The present study investigated whether the two hypotheses of inhibition control and visual form perception could explain the relationship between kindergarteners' ANS and mathematical achievements. In spring, data were collected from a sample of 180 kindergarteners (Mage = 5.77 years, SD = 0.59). A parallel mediation analysis was conducted to investigate the role of inhibition control and visual form perception in the link between ANS and math achievement. The results indicated an indirect effect of ANS on mathematical achievements through both inhibition control and visual form perception, with both mediators exhibiting a comparable magnitude. These findings highlight the significance of distinct cognitive abilities that can potentially enhance early mathematical advancement. [ABSTRACT FROM AUTHOR]

The rough set model has been extended to interval rough number decision systems, but the existing studies do not consider interval rough number decision systems with missing values. To this end, a rough set model of incomplete interval rough number decision systems (IIRNDSs) is proposed, and its uncertainty measures are investigated. Firstly, the similarity of two incomplete interval rough numbers (IIRNs) are defined by calculating their optimistic and pessimistic distances of the lower and upper approximation intervals of IIRNs. Then, the rough sets in IIRNDSs are constructed by the induced similarity relation. Next, four uncertainty measures, including approximation accuracy, approximation roughness, conditional entropy, and decision rough entropy are given, which exhibit a monotonic variation with changes in the size of attribute sets, α, and θ. Finally, the experimental results demonstrate the proposed rough set model of IIRNDSs is feasible and effective. [ABSTRACT FROM AUTHOR]

We test children's distributive and collective sentence interpretations and the variables that predict them. In our first experiment, we establish that adult English collective sentences with the or some in the subject are categorically collective in their interpretations. We further demonstrate that children's collective and distributive interpretations are predicted by an independent measure of lexical growth, consistent with the lexical refraction hypothesis, and that their collective interpretations are predicted by their distributive interpretations, consistent with the pragmatic scale hypothesis. Furthermore, the distributive interpretations produce complete mediation between lexicon and collective interpretations in a mediation analysis. In our second experiment, we take independent measures of Spanish-speaking children's knowledge of the Approximate Number System, inhibition, lexicon and phrasal syntax. We then fit a Piecewise Structural Equation Model with these variables, with high statistical power and showing high goodness-of-fit. We consider the contrast between this model of collective interpretations, which are putatively conversational implicatures, and quantity implicature models from previous studies. [ABSTRACT FROM AUTHOR]

A generalized construction procedure for algebraic number systems is hereby presented. This procedure offers an efficient representation and computation method for complex numbers, quaternions, and other algebraic structures. The construction method is then illustrated across a range of examples. In particular, the novel developments reported herein provide a generalized form of the Cayley–Dickson construction through involutive dimagmas, thereby allowing for the treatment of more general spaces other than vector spaces, which underlie the associated algebra structure. [ABSTRACT FROM AUTHOR]

Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u ~ ,   u ~ ⊗ 1 u ~ = i ~ = (1 , 1 , 0 , 0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u ~ is constructed 1 u ~ so that u ~ ⊗ 1 u ~ = i ~ = (1 , 1 , 0 , 0) . Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m × m . We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m × n with m   ≠ n . This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention. [ABSTRACT FROM AUTHOR]

Multiple pulse charging modules were designed and tested for synchronous use in scaled experiments. The pulse chargers are each capable of charging a nanofarad-sized capacitive load to 100 kV in less than 10 µs. This is achieved by initially charging a microfarad-sized capacitor to a maximum of 3 kV, then, using a thyristor switch, discharging the capacitor into two transformers paralleled on the primary side. Each transformer steps the voltage up to 50 kV, with the transformer having opposing polarities and a common neutral on the secondary. Thus, the full 100 kV is obtained by placing the nanofarad-sized capacitor between the +50 and −50 kV terminals. The pulse chargers use a microcontroller to monitor and control the pulse charger in addition to communicating with the user as well as other pulse chargers. For increased battery life, each pulse charger is kept in a low-power state while not in use. Upon startup, the pulse chargers automatically detect the number of modules in the system, the position of itself in the system, and the timing delays associated with each pulse charger in the system. This information is essential for synchronous charging and provides individual information and controls for the pulse chargers. [ABSTRACT FROM AUTHOR]

We present a study of the detection efficiency for the TESS mission, focusing on the yield of longer period transiting exoplanets (P > 25 d). We created the Transit Investigation and Recoverability Application (TIaRA) pipeline to use real TESS data with injected transits to create sensitivity maps which we combine with occurrence rates derived from Kepler. This allows us to predict longer period exoplanet yields, which will help design follow-up photometric and spectroscopic programs, such as the NGTS (Next Generation Transit Survey) Monotransit Program. For the TESS Years 1 and 3 SPOC (Science Processing Operations Centre) FFI (Full Frame Image) light curves, we find |$2271^{+241}_{-138}$| exoplanets should be detectable around AFGKM dwarf host stars. We find |$215^{+37}_{-23}$| exoplanets should be detected from single-transit events or 'monotransits'. An additional |$113^{+22}_{-13}$| detections should result from 'biennial duotransit' events with one transit in Year 1 and a second in Year 3. We also find that K dwarf stars yield the most detections by TESS per star observed. When comparing our results to the TOI (TESS objects of interest) catalogue, we find our predictions agree within 1σ of the number of discovered systems with periods between 0.78 and 6.25 d and agree to 2σ for periods between 6.25 and 25 d. Beyond periods of 25 d, we predict |$403^{+64}_{-38}$| detections, which is three times as many detections as there are in the TOI catalogue with >3σ confidence. This indicates a significant number of long-period planets yet to be discovered from TESS data as monotransits or biennial duotransits. [ABSTRACT FROM AUTHOR]

Porous liquids combine the properties of a porous solid with those of a liquid, creating a porous flowable media. Since their discovery, these materials have gathered widespread interest within the scientific community, with substantial numbers of new systems being discovered, often with a focus on increasing the pore volume and gas capacity. Which begs the question, what does the future hold for porous liquids? Recently, the first examples of photoresponsive porous liquids have emerged, allowing changes in porosity to be observed under UV irradiation. Here, we expand on our previous report of photoresponsive porous liquids and explore the conceptualisation of responsive porous liquids and how these materials could be developed with the ability to respond to light, thereby offering a potential mechanism of controllable uptake and release in these systems. This concept article summarises different approaches that could be used to incorporate a photoresponse in a porous liquid before discussing recently reported systems, alongside important factors to consider in their design. Finally, by taking inspiration from the methods used to translate porous solids into the liquid state, combined with the field of photoresponsive materials, we discuss potential strategies that could be employed to realise further examples of photoresponsive porous liquids. [ABSTRACT FROM AUTHOR]

In this paper, we consider a genetic evolution model associated to a given Feynman–Kac flow (called also the simple genetic algorithm). We first obtain an estimate of the contraction coefficient of this interacting particle system in some suitable metric, independent of the number of particles in the system. Second, by transport-entropy inequality technique, we obtain some concentration inequalities for the particle system, uniform in time and in the number of particles. [ABSTRACT FROM AUTHOR]

Stellar coronal sources have been observed in the past not only for their astrophysical interest in the field of binary system evolution and interaction but also for their invaluable roles as benchmarks for plasma spectral models and as calibration sources for high resolution spectroscopic X-ray instruments. These include the gratings on-board Chandra and XMM-Newton , as well as the new generation of high resolution capable-detectors recently flown on-board XRISM and planned for the future also onboard the Athena and the LEM missions. In our previous paper exploiting Chandra /HETG observations of the prototypical coronal source Capella, it has been shown that the centroid energies of the many X-ray emission lines detected in the spectrum of this object change as a function of time due to the Doppler modulation within the binary. This is an effect that needs to be corrected while performing calibrations of high-resolution X-ray instruments. In this paper, we extend our previous work on Capella to other known stellar coronal sources that have been observed with the Chandra /HETG (11 objects in total). We measure in several objects clear trends in the velocity shifts along the orbit of the primary star, meaning that in these sources one of the two star components is largely dominating the high energy emission. In a number of systems the trend in the velocity shift is not obvious. This can be ascribed to the fact that both stellar components contribute significantly to the X-ray emission. [ABSTRACT FROM AUTHOR]

To simulate quantum systems on classical or quantum computers, the continuous observables (e.g., coordinate and momentum or energy and time) must be reduced to discrete ones. In this paper, we consider the continuous observables represented in the positional systems as power series in the radix multiplied over the summands ("digits"), which turn out to be Hermitian operators with discrete spectrum. We investigate the obtained quantum mechanical operators of digits, the commutation relations between them, and the effects of the choice of a numeral system on lattices and representations. Renormalizations of diverging sums naturally occur in constructing the digital representation. [ABSTRACT FROM AUTHOR]

In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems. [ABSTRACT FROM AUTHOR]

"Allosteric" was first introduced to mean the other site (i.e., a site distinct from the active or orthosteric site), an adjective for "regulation" to imply a regulatory outcome resulting from ligand binding at another site. That original idea outlines a system with two ligand-binding events at two distinct locations on a macromolecule (originally a protein system), which defines a four-state energy cycle. An allosteric energy cycle provides a quantifiable allosteric coupling constant and focuses our attention on the unique properties of the four equilibrated protein complexes that constitute the energy cycle. Because many observed phenomena have been referenced as "allosteric regulation" in the literature, the goal of this work is to use literature examples to explore which systems are and are not consistent with the two-ligand thermodynamic energy cycle-based definition of allosteric regulation. We emphasize the need for consistent language so comparisons can be made among the ever-increasing number of allosteric systems. Building on the mutually exclusive natures of an energy cycle definition of allosteric regulation versus classic two-state models, we conclude our discussion by outlining how the often-proposed Rube-Goldberg-like mechanisms are likely inconsistent with an energy cycle definition of allosteric regulation. [ABSTRACT FROM AUTHOR]