The article studies fast algorithms for numerical modeling of problems with random input data. The approaches under consideration are non-intrusive methods based on probabilistic extensions. They rely on existing numerical methods for solving deterministic problems and use them as solvers. Unlike polynomial chaos methods, in some cases it is possible to avoid exponential growth of the number of operations from the number of input parameters.
Big-step semantics is presented for the language that is powerful enough to encode arbitrary formal systems with computable inference rules and metatheorems about them but simple enough to implement and to reason about and potentially suitable for self-verification.
In this article, matrix analogues of the general properties of the Laplace transform for the classical domains of second type are established. In particular, the theorem on the holomorphicity of the image function, the uniqueness theorem for original function, and an explicit inverse Laplace transform formula are derived in the matrix setting. Furthermore, new properties specific to the classical domains of second type are obtained and rigorously proved using direct matrix differential operators.
We study the satisfiability problem for a bimodal temporal logic interpreted on infinite cluster frames of the form W = & sqcup;iEN C(i). Each cluster C(i) is an arbitrary (possibly infinite) Kripke frame with a reflexive and transitive local relation, while the global relation linearly orders the clusters and represents a discrete macro-time. We prove decidability of the logic by a two-stage reduction. First, we apply local filtration with respect to the set of subformulas that do not contain global modalities; this compresses the internal structure of each cluster while preserving truth of the local fragment. Second, we establish the existence of a stability index and the correctness of a folding procedure, which replaces an infinite sequence of clusters by a finite lasso-shaped structure without loss of truth for the input formula. Correctness of folding is proved by induction on the temporal degree of a formula (the nesting depth of the global modality). As a consequence, we obtain a finite-model property with respect to the constructed class of filtered lassos and an effective satisfiability-checking procedure.
A correction algorithm has been developed to preserve required motion invariants at each step of numerical integration of gravitational N-body problem, independent of the underlying numerical integration method. The effectiveness of the proposed algorithm is demonstrated using the Kepler problem as an example. Specifically, it is shown that the algorithm extends the applicability range of classical integrators of lower order.
The paper presents a study of a queuing system with two service units, an unlimited number of servers, and a non-stationary arrival Poisson process as a mathematical model of a hybrid power system combining two energy sources. The transient asymptotic method is proposed for the deriving the time-dependent formulas for the probability distribution of the number of customers in the system under the limit condition of a high arrival rate. Gaussian form of the asymptotic probability distribution of the number of customers in the system is proved. The results of the numerical analysis are presented.
This article discusses an algorithm for optimal spatiotemp oral processing of navigation parameters in the presence of interference. The problem of estimating radio navigation parameters in GNSS receivers equipped with an antenna array is addressed. An optimal adaptive algorithm for determining navigation parameters using an antenna array based on GNSS signals in an unknown interference environment is synthesized. The main approaches to improving the computational efficiency of adaptive spatial-temporal processing algorithms in GNSS receivers are presented. It is shown that recursive updating of the R matrix using the QR factorization based on Givens rotations significantly improves computational efficiency. Examples of applying the CORDIC algorithm to recursive estimation of the R matrix and antenna array weights are given.
We report the existence of three superconducting subsystems in samples of high-temperature superconductor YBa(2)Cu(3)O(7-delta )doped by NiO nanoparticles and then subjected to 18-hour annealing. These subsystems exhibit different superconducting transition temperatures and respond differently to magnetic fields. While two-level superconductivity formed by grain and intergranular boundary subsystems is known in polycrystalline superconductors, our material reveals an additional subsystem formed by surface layers of grains with reduced critical temperature and enhanced sensitivity to magnetic field.
This paper is devoted to multidimensional analogues of Ostrovsky's theorem on lacunary series. The work examines the domains of existence of Hartogs lacunary series with Ostrovsky lacunae and series in homogeneous polynomials. Analogues of Ostrovsky's theorem for such series are given and the domains of convergence of these series are described.
In this work, gold nanoparticles were synthesized by two methods: the Turkevich-Frens method and seed-mediated growth method. The features of each method and their effect on the size, morphology, and optical properties of the obtained particles are described. The dependence of the plasmon resonance wavelength on the shape of nanoparticles has been analysed using optical spectroscopy. It has also been shown that changes in synthesis conditions affect the spectral characteristics of colloidal gold.
The work is devoted to the study of the real roots of a system of transcendental equations arising in the Frank-Kamenetskii model. It is shown that the number of real roots is related to the number of real roots of some entire function (resultant). The number of complex roots is investigated.
Approximate solution of a boundary-value problem for a model of the far swirling turbulent wake past a self-propelled body is constructed using asymptotic expansion of the solution in a neighbourhood of the singular point. A good agreement between constructed solution and numerical solution is obtained.
Let pound be a positive integer. In this paper, we prove a new explicit formula for the generalized Bernoulli polynomials of order pound. This formula generalizes many known identities for the Bernoulli polynomials. Our main tools are linear operators.
The sufficient conditions of solution existence are established for the inverse problem of finding a piecewise constant coefficient in the second-order elliptic equation with the Dirichlet boundary condition and the integral overdetermination condition on the boundary of the domain under consideration.
Starting from Kurepa's function and the hypothesis of divisibility to Gamma function, their thermodinamical analogies are constructed and their properties are compared to the one found for Riemann's Zeta function.
In current paper we present numerical evaluations of electrovortex flows in a melt of In-Ga-Sn. A hemispherical copper container is filled with the melt. The flows were induced by applying low frequency (0.1-20 Hz) alternating current. Velocity, temperature, and mass concentration of the same melt admixture were obtained. An influence on the motion and heat transfer by the sinusoidal current was demonstrated.
In [2], the author introduced the notion of P-compactness via the primal structure. This paper extends that work by defining and exploring P-Lindelofness in primal topological spaces, establishing its main properties and providing some results as natural generalizations of covering properties within the primal framework.
The first-principles calculations of the structural and magnetic properties of kotoite Ni2Co(BO3)(2) have been carried out. The minimization of the lattice parameters shows the values toto be in good agreement with the experimental data (the difference is less than 1%). The atomic coordinates have been calculated. Cobalt ions tend to occupy position 2a and nickel ions tend to occupy position 4f. The same magnetic cell as in Ni3B2O6 but quadrupled in size (2a & times; b & times;2c) has the minimum exchange energy for Ni2Co(BO3)(2). In Ni2Co(BO3)(2 ), the magnetic moments are oriented along the b axis as in Co3B2O6.
Since the beginning of the last century, non-associative algebraic systems have been used to coordinatize non-Desarguesian projective translation planes. Such systems as semifields and quasifields are now find application in cryptographic algorithm design. Hall quasifields were introduced in 1943 and were the first examples of non-distributive and non-associative quasifields. They are two-dimensional quasifields over the center, all non-central elements of which satisfy unique quadratic equation. The automorphism group acts transitively on non-central elements. Hall quasifields of the same order coordinatize the isomorphic translation planes, that is Hall planes. Increasing the dimension of the quasifield over the center, we obtain generalized quasifields with the Hall condition. Such a quasifield cannot be either a semifield or a near-field. More than one non-isomorphic quasifields with the Hall condition can correspond to one irreducible polynomial over a given field. The spread set method is used for reasoning and calculations. It allows to present the multiplication rule as a linear transformation and so to describe subfields and sub-quasifields, spectra and automorphisms. These structural questions with some solutions are naturally transferred from the two-dimensional case. Unlike Hall quasifields, a multidimensional quasifield with the Hall condition cannot be generated by a single element, this fact completes the results by M. Cordero and V. Jha (2009) on covering and primitivity. Presenting examples, the authors list all non-isomorphic quasifields of order 16 with the Hall condition and define their automorphism groups.
We present a method for the efficient computation of weighted sums over the sets of nonnegative integer solutions to linear systems of a specific form. Our main result is an explicit formula that evaluates such sums through a discrete analogue of the Newton-Leibniz operator. This formula serves as a powerful tool for tackling combinatorial problems. To illustrate the effectiveness of our approach, we apply it to classical examples, including the problem of counting lucky tickets.
