Conditions For Uniqueness Research Articles

The Inverse Eigenvalue Problem for a Class of Sub-periodic Generalized Jacobi Matrices

The inverse eigenvalue problem of matrix has practical significance in engineering and scientific calculation. In this paper, the inverse eigenvalue problem of sub-periodic generalized Jacobi matrices is studied. Two eigenvalues and corresponding eigenvectors are used to construct generalized Jacobi matrices. The existence and uniqueness conditions of the solution are discussed, the solution algorithm for the inverse problem is given, and the effectiveness of the algorithm is verified by a numerical example.

Removable isolated singularities for anisotropic of anisotropic evolution p-Laplacian equation

In this paper we study nonnegative weak solutions of a quasilinear parabolic equations in a divergent form, one of the model cases of which is anisotropic evolution p-Laplacian equation. New pointwise estimates near an isolated singularity and sufficient condition of the removability of isolated singularity were obtained.

Existence and uniqueness of recursive utilities without boundedness

This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of (stochastic) recursive utilities for several important classes of preferences. In order to accommodate models commonly used in practice, we allow both the state space and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single, primitive “thin tail” condition on the distribution of growth in per-period utilities. We present several applications to robust preferences, models of ambiguity aversion and learning about hidden states, and Epstein–Zin preferences.

New Uniqueness Conditions for the Stationary Probability Matrix of Transition Probability Tensors

New Uniqueness Conditions for the Stationary Probability Matrix of Transition Probability Tensors

Dynamic pricing and advertising in the presence of strategic consumers and social contagion: A mean-field game approach

In this paper, we introduce a framework for new product diffusion that integrates consumer heterogeneity and strategic social influences at individual level. Forward-looking consumers belong to two mutually exclusive segments: individualists, whose adoption decision is influenced by the price and reputation of the innovation, and conformists, whose adoption decision depends on social influences exerted by other consumers and on the price. We use a mean-field game approach to translate consumer strategic interactions into aggregate social influences that affect conformists’ adoption decision. The game is played à la Stackelberg, with the firm acting as leader and consumers as followers. The firm determines its pricing and advertising strategies to maximize its profit over a finite planning horizon. We provide the conditions for existence and uniqueness of equilibrium and a numerical scheme to compute it. We conduct a series of numerical simulations to analyze firm’s strategy and diffusion processes for different parameter constellations. Our results suggest that the firm adopts a penetration pricing strategy in the presence of strategic consumers, whereas it decreases the price first and then increases it in face of myopic consumers. Moreover, our model asserts that diffusion of innovations is considerably shaped by the consumer heterogeneity. Indeed, our results show that as the fraction of one segment increases in the market, the consumers in the other segment have less tendency towards adoption.

Topological entropy of composition and impulsive differential equations satisfying a uniqueness condition

The impulsive differential equations are examined via the associated Poincaré translation operators in terms of topological entropy. The crucial role is played by the entropy analysis of the compositions of Poincaré’s operators with the impulsive maps. For the scalar (one-dimensional) problems, the lower entropy estimations can be effectively obtained by means of horseshoes. For the vector (higher-dimensional) problems, the situation becomes more delicate and requires rather sophisticated techniques. Five main theorems are presented about a positive topological entropy (i.e. topological chaos) for given impulsive problems. For vector linear homogeneous differential equations with constant coefficients and isometric impulses, the zero entropy is deduced under commutativity restrictions imposed on the components of a mentioned composition. Several illustrative examples and numerical simulations are supplied.

Complicated Grief After the Loss of a Baby: A Systematic Review About Risk and Protective Factors for Bereaved Women

This study sought to identify the factors associated with the development and prevention of complicated grief in women who have lost a baby. This is a systematic review of scientific articles in the main mental health databases: MEDLINE (PubMed), EMBASE, Latin American and Caribbean Health Sciences Literature (LILACS), and APA Databases (PsycINFO). The selection and data extraction processes occurred independently and blindly by two authors, considering the eligibility criteria. The analysis included publications from 2013 to 2021 of observational studies with adult women who had experienced losing a baby (during pregnancy up to 2 years of life) and that employed standardized instruments to evaluate grief. From the 8,200 records found, 23 articles were selected for analysis. As risk factors, we identified the presence of mother’s psychopathology, history of gestational loss, and social pressure for a new pregnancy, while as protective factors, we identified the presence of another child other than the deceased one, the quality of specialized healthcare, and the social support provided by either a partner, community, or spiritual activities. Furthermore, the studies pointed to the event of losing a baby as an opportunity for posttraumatic growth. Although complicated grief is often associated with other mental health conditions, such as anxiety, depression, or posttraumatic stress, it is necessary to differentiate it for a clearer understanding of the complicated grief as a singular condition, to enable access to appropriate care for bereaved mothers and families, as well as to promote public policies which provide support to them.

Applied Mechatronics: On Mitigating Disturbance Effects in MEMS Resonators Using Robust Nonsingular Terminal Sliding Mode Controllers

This investigation attempts to study a possible controller in improving the dynamic stability of capacitive microstructures through mitigating the effects of disturbances and uncertainties in their resultant dynamic behavior. Consequently, a nonsingular terminal sliding mode control strategy is suggested in this regard. The main features of this particular control strategy are its high response speed and its non-reliance on powerful controller forces. The stability of the controller was investigated using Lyapunov theory. For this purpose, a suitable Lyapunov function was introduced to prove the stability of a controller, and the singularity conditions and methods to overcome these conditions are presented. The achieved results proved the high capability of the applied technique in stabilizing of the microstructure as well as mitigating the effects of disturbances and uncertainties.

Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Uniqueness conditions and fitting methods have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms, $R$, and their individual ranks, $L_r$, has only recently started to attract significant attention, mainly through regularization-based approaches which entail the need to tune the regularization parameter(s). In this work, we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level \emph{hierarchical} probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is \emph{jointly} imposed. Ranks are then estimated from the numbers of blocks ($R$) and columns ($L_r$) of non-negligible energy. Approximate posterior inference is implemented, within the variational inference framework. The resulting iterative algorithm completely avoids hyperparameter tuning, which is a significant defect of regularization-based methods. Alternative probabilistic models are also explored and the connections with their regularization-based counterparts are brought to light with the aid of the associated maximum a-posteriori (MAP) estimators. We report simulation results with both synthetic and real-word data, which demonstrate the merits of the proposed method in terms of both rank estimation and model fitting as compared to state-of-the-art relevant methods.

Uniqueness conditions and numerical approximation of the solution to M.M. Lavrentiev's integral equation

Uniqueness conditions and numerical approximation of the solution to M.M. Lavrentiev's integral equation

Equilibrium Defaultable Corporate Debt and Investment

In dynamic capital structure models with an investor break-even condition, the firm's Bellman equation may not generate a contraction mapping, so the standard existence and uniqueness conditions do not apply. First, we provide an example showing the problem in a classical trade-off model. The firm can issue one-period defaultable debt, invest in capital and pay a dividend. If the firm cannot meet the required debt payment, it is liquidated. Second, we show how to use a dual to the original problem and a change of measure, such that existence and uniqueness can be proved. In the unique Markov-perfect equilibrium, firm decisions reflect state-dependent capital and debt targets. Our approach may be useful for other dynamic firm models that have an investor break-even condition.

Free boundary Monge-Ampère equations

In this paper, we consider a class of Monge-Ampère equations in a free boundary domain of ℝ2 where the value of the unknown function is prescribed on the free boundary. From a variational point of view, these equations describe an optimal transport problem from an a priori undetermined source domain to a prescribed target domain. We prove the existence and uniqueness of a variational solution to these Monge-Ampère equations under a singularity condition on the density function on the source domain. Furthermore, we provide regularity results under some conditions on the prescribed domain.

Dynamic Behavior of a Stochastic Tungiasis Model for Public Health Education

In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation.

INVERSE SOURCE PROBLEM FOR A SEMILINEAR FRACTIONAL DIFFUSION-WAVE EQUATION UNDER A TIME-INTEGRAL CONDITION

We study the inverse boundary value problem on determining a space-dependent component in the right-hand side of semilinear time fractional diffusion-wave equation. We find sufficient conditions for a time-local uniqueness of the solution under the time-integral additional condition \[\frac{1}{T}\int_{0}^{T}u(x,t)\eta_1(t)dt=\Phi_1(x), \;\;\;x\in \Omega\subset \Bbb R^n\] where $u$ is the unknown solution of the first boundary value problem for such equation, $\eta_1$ and $\Phi_1$ are the given functions. We use the method of the Green's function.

On the Efficiency of Decentralized Epidemic Management and Application to Covid-19

In this letter, we introduce a game that allows one to assess the potential loss of efficiency induced by a decentralized control or local management of a global epidemic. Each player typically represents a region or a country which is assumed to choose its control action to implement a tradeoff between socio-economic aspects and the health aspect. We conduct the Nash equilibrium analysis of this game. Since the analysis is not trivial in general, sufficient conditions for existence and uniqueness are provided. Then we quantify through numerical results the loss induced by decentralization, measured in terms of price of anarchy (PoA) and price of connectedness (PoC). These results allow one to clearly identify scenarios where decentralization is acceptable or not regarding to the retained global efficiency measures.

Study of multi term delay fractional order impulsive differential equation using fixed point approach

<abstract><p>This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.</p></abstract>

Results on Implicit Fractional Pantograph Equations with Mittag‐Leffler Kernel and Nonlocal Condition

In this study, the main focus is on an investigation of the sufficient conditions of existence and uniqueness of solution for two‐classess of nonlinear implicit fractional pantograph equations with nonlocal conditions via Atangana–Baleanu–Riemann–Liouville (ABR) and Atangana–Baleanu–Caputo (ABC) fractional derivative with order σ ∈ (1,2]. We introduce the properties of solutions as well as stability results for the proposed problem without using the semigroup property. In the beginning, we convert the given problems into equivalent fractional integral equations. Then, by employing some fixed‐point theorems such as Krasnoselskii and Banach’s techniques, we examine the existence and uniqueness of solutions to proposed problems. Moreover, by using techniques of nonlinear functional analysis, we analyze Ulam–Hyers (UH) and generalized Ulam–Hyers (GUH) stability results. As an application, we provide some examples to illustrate the validity of our results.

On degree theory for non-monotone type fractional order delay differential equations

<abstract><p>In this paper, we establish a qualitative theory for implicit fractional order differential equations (IFODEs) with nonlocal initial condition (NIC) with delay term. Because area related to investigate existence and uniqueness of solution is important field in recent times. Also researchers are using existence theory to derive some prior results about a dynamical problem weather it exists or not in reality. In literature, we have different tools to study qualitative nature of a problem. On the same line the exact solution of every problem is difficult to determined. Therefore, we use technique of numerical analysis to approximate the solutions, where stability analysis is an important aspect. Therefore, we use a tool from non-linear analysis known as topological degree theory to develop sufficient conditions for existence and uniqueness of solution to the considered problem. Further, we also develop sufficient conditions for Hyers- Ulam type stability for the considered problem. To justify our results, we also give an illustrative example.</p></abstract>

Grid-Forming Hybrid Angle Control and Almost Global Stability of the DC-AC Power Converter

This paper introduces a new grid-forming control for a grid-connected dc-ac power converter, termed hybrid angle control (HAC) that combines the dc-based matching control with a novel nonlinear angle feedback reminiscent of (though not identical to) classic droop control. The synthesis of HAC is inspired by the complementary benefits of the dc-based matching and ac-based grid-forming controls as well as ideas from direct angle control and nonlinear damping assignment. The proposed HAC is applied to a nonlinear converter model that is connected to an infinite bus or a center-of-inertia dynamic grid models. We provide parametric sufficient existence, uniqueness, stability, and boundedness conditions that are met by appropriate choice of control parameters. Next, we take into account the safety constraints of power converter, and synthesize a new current-limiting control that is compatible with HAC. Last, we present details on the practical implementation of HAC that are followed by a robustness analysis (which showcases a theory-practice gap), uncover the intrinsic droop behavior of the HAC, derive a feedforward-like ac voltage and power control, and illustrate the behavior of the closed-loop system with simulation case studies.

Continuity problem for singular BSDE with random terminal time

We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition $\xi$ is allowed to take the value +$\infty$, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a solution, i.e., attains the terminal values with probability 1. We consider three types of terminal values: 1) Markovian: i.e., $\xi$ is of the form $\xi$ = g($\Xi$ S) where $\Xi$ is a continuous Markovian diffusion process and S is a hitting time of $\Xi$ and g is a deterministic function 2) terminal conditions of the form $\xi$ = $\infty$ $\times$ 1 {$\tau$ $\le$S} and 3) $\xi$ 2 = $\infty$ $\times$ 1 {$\tau$ >S} where $\tau$ is another stopping time. For general $\xi$ we prove the minimal supersolution is continuous at time S provided that F is left continuous at time S. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value $\infty$ at terminal time S. The concept of solvability plays a key role in many of the arguments. Finally, we discuss implications of our results on the Markovian terminal conditions to solution of nonlinear elliptic PDE with singular boundary conditions.