By using the condition of formation of internal resonances for steady-state liquid sloshing in toroidal tanks caused by the resonance excitation of the lowest eigenfrequency, we determine the set of input geometric parameters for which the secondary resonance phenomenon may lead to the amplification of higher modes. We formulate a series of recommendations for the forthcoming development of nonlinear modal methods for tanks of given shapes.
We generalize the classical Levinson theorem on the asymptotic equivalence on infinite-dimensional stochastic systems. In particular, for a given system of linear stochastic differential equations, we construct a system of ordinary differential equations whose solutions are characterized by the behavior at infinity similar to the behavior of solutions of the original system both in the mean-square sense and with probability 1.
We construct a system of difference equations aimed at the description of the dynamics of regional redistribution and numerical losses for the alternative opponents struggling for the presence in the common territory. In terms of the strategies of ordered initial distributions, we establish a series of sufficient conditions guaranteeing the minimization of losses in a simple model with three regions. Computer simulations are carried out for a specific example.
We consider the Cauchy problem for a linear inhomogeneous set-valued differential equation with Hukuhara derivative and constant coefficients and obtain its solution in the analytic form.
We study a two-point boundary-value problem for a singularly perturbed differential-algebraic system in the case of simple roots of the characteristic equation. We also establish sufficient conditions for the existence and uniqueness of solution to this boundary-value problem and present its asymptotic expansion.
We propose an analytic method for solving a three-dimensional dynamic problem of propagation of elastic vibrations in a circular bounded plate under the action of instantaneous internal dilation ε* (instantaneous relative variation of an infinitely small volume) appearing, e.g., as a result of contact welding of plates. This problem appears in connection with the problem of decoding acoustic-emission signals in the course of prediction of the residual life of commercial welded metal objects hazardous under operating conditions with the help of acoustic-emission systems based on the use of circular piezoelectric sensors.
The task of solving of nonlinear equations often involves the use of iterative methods that require multiple inversions of linear operators, which can be computationally costly, especially for large matrices or complex operators. We propose hybrid two-point methods that overcome the indicated limitation by requiring only a single inversion of a fixed linear operator throughout the entire process. This approach preserves the rapid convergence and avoids the repeated inversions of Q′(yn) in each step. We provide both semilocal and local convergence analyses, utilizing a majorant function to control the Fréchet derivative of the operator. Numerical experiments confirm that the performance of our methods is comparable with the classical approaches but is characterized by much lower computational costs. These findings highlight the potentials of this technique as a practical alternative to Newton’s method and other iterative methods requiring operator inversions.
We investigate the convexity and monotonicity properties for two classes of analytic functions related to the Le Roy-type hypergeometric function. Numerical examples and graphical illustrations support our theoretical findings and motivate a propositionsed conjecture.
We study the topological properties, possible structures, classifications, and encoding of the flows on a two-dimensional disk, which have finitely many separatrices in the case where all singular points of the flows lie on the boundary of the disk. Trees with selected leaves are used for the classification of these flows. We construct a code for the flow with one singular point on the boundary. All possible structures of these flows with one singular point and at most five separatrices are described.
We introduce the monophonic global domination number γ_m(G) by combining monophonic convexity (via chordless paths) with the global domination in a graph and its complement. A monophonic global dominating set is defined, and γ_m(G) is regarded as the minimum size of sets of this kind. We also establish the bounds, relate γ_m(G) to the classical domination number, and characterize the graphs that attain extreme values. The realization theorem is proved for prescribed parameter values. The behavior of γ_m(G) under graph operations, in particular, for the corona product, is analyzed. The applications to the network monitoring are discussed and several open problems are proposed for further research.
Beer and Ok showed that a locally compact and order-connected Hausdorff topological semilattice X can be embedded in the space of all closed subsets of X endowed with the Fell topology and ordered by set inclusion. First, we show that this result can be generalized to the case of Hausdorff semitopological semilattices. Second, we also prove that a locally compact Hausdorff semitopological semilattice is a topological poset. Third, we conclude that a mapping defined by x → ↓x from a locally compact lower semiclosed space (X, τ, ≤) to the space of all closed subsets of X endowed with the Fell topology and ordered by set inclusion is continuous if and only if X is upper open and ≤ is closed in X × X. Finally, we introduce the concept of H-closedness for a T0 topological space.
We introduce admissible Mannheim partner curves according to a modified orthogonal frame in the 3-dimensional Galilean space G3. Moreover, we use a modified orthogonal frame according to torsion. Further, we analyze these partner curves with respect to the modified orthogonal frame by curvature and torsion and obtain some characterizations of these curves. These findings have led us to the discovery of some curious remarks concerning Mannheim curves.
We introduce the windowed linear canonical Lions transform, which generalizes the classical Lions transform introduced in [K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal., 4, No. 1, 97–112 (1997)]. Some basic properties, such as Plancherel, inversion, and convolution theorems involving this integral operator are formulated and proved. In addition, the Donoho–Stark uncertainty principle, the Lieb uncertainty principle, and the Heisenberg-type inequality via the k-entropy are discussed and proved for the proposed transform.
Let 𝒮_cos^* be a class of normalized analytic functions f in an open unit disk 𝔻 satisfying the subordination zf'(z)/f(z)≺cosz . The aim of the present article is to find upper bounds for the module of some coefficients, of the fourth Hankel determinant H4,1(f) for the function class 𝒮_cos^* , and of some functionals defined by using the expansion coefficients in Taylor series. Moreover, we also find the upper bounds for the fifth and sixth logarithmic coefficients obtained for the functions from the same class. Note that some of our results are the best possible. The results of our paper improve numerous versions of the results recently presented in [K. Marimuthu, J. Uma, and T. Bulboacă, Hacet. J. Math. Stat., 52, No. 3, 596 (2023)]. The tools used in the proofs have been recently obtained in [N. E. Cho, B. Kowalczyk, A. Lecko, and B. Śmiarowska, Filomat, 34, No. 6, 2061 (2020)]. They are combined with the results from [F. Carlson, Ark. Mat. Astr. Fys., 27A, No. 1, 8 (1939)], and with the method aimed at finding the extrema of real functions of many variables.
We deduce an affine dual log-Minkowski inequality by introducing two new concepts of dual affine measure and Orlicz dual affine measure and using the newly established Orlicz dual affine Minkowski inequality. In a special case, the Orlicz affine dual log-Minkowski inequality yields the Lp-affine dual log-Minkowski inequality. The affine dual log-Minkowski inequality is also obtained.
We study the Lie symmetries of a class of systems of (1 + 1)-dimensional nonlinear diffusion equations. The equivalence algebra and the kernel of the maximal Lie invariance algebras of this class are found. We prove that there exist exactly nine inequivalent subclasses of this class for which the corresponding diffusion systems admit Lie symmetry extensions. We also propose the exhaustive group classification of the systems of nonlinear diffusion equations from the first subclass.
We consider substitutions reducing nonlinear heat equations with a source to a system of two ordinary differential equations. Classes of exact solutions of these equations with generalized separation of variables are constructed.
We study Bott–Duffin (e, f)-inverses in the context of left and right semi-central idempotents. A new class of generalized inverses named semi-central Bott–Duffin (e, f)-inverses is introduced and studied. An example is given to show that Bott–Duffin (e, f)-inverses are not necessarily semi-central Bott–Duffin (e, f)-inverses. It is shown that the semi-central Bott–Duffin (e, f)-inverses exhibit additional properties beyond the properties of general Bott–Duffin (e, f)-inverses. As applications, we examine semi-central Bott–Duffin (e, f)-inverses for several classes of matrices.
We study the problem of optimal control of the Goursat–Darboux-type differential inclusions (DFIs) given by polyhedral set-valued mappings and, for this purpose, pose an auxiliary problem with discrete Goursat–Darboux inclusion. By using the Farkas theorem, we compute locally adjoint mappings (LAMs) and establish necessary and sufficient optimality conditions for the polyhedral discrete Goursat–Darboux inclusions. Further, by the discretization method, for the Goursat–Darboux-type polyhedral DFI, we formulate (by using solely the specific features of its polyhedral property), first for a discrete-approximate problem and then, for a continuous problem, necessary and sufficient optimality conditions in the form of Euler–Lagrange-type polyhedral inclusions.
The theory of multiplicative calculus has recently gained loads of attention. In this framework, the operations of addition and subtraction are systematically replaced with multiplication and division, respectively. The interest in this system is to obtain a multiplicative analog of the results obtained in the classical sense. Our aim is to contribute to the body of knowledge in this direction. Specifically, we establish some novel generalizations of the Hermite–Hadamard–Mercer-type inequalities involving new multiplicative tempered fractional integrals. A new lemma is also established. By using this lemma, Hölder’s inequality, and the power-mean inequality, we obtain more inequalities of the Trapezoid–Mercer type. Our results generalize many other results available from the literature. We present some numerical examples, utilizing the Wolfram Mathematica software for computations and graphing, to prove the validity of our results by comparing the outcomes for different values of the operating parameter λ ∈ [0, 1] with 0.1 as the step size. Finally, we obtain additional estimates by applying our results to special means, such as arithmetic, harmonic, logarithmic, and p-logarithmic means.
