Conditions For Uniqueness Research Articles

A New Soft Computing Fractal Model for Cancer Treatment with Fractal - Fractional Operators

In the current work, we represent a new soft computing cancer model with the help of Fractal Fractional operators. In this paper, we used the nonlinear system. The numerical scheme we have applied which is a new method. This proposed methods we have applied for different Fractal Fractional operators. The existence and uniqueness conditions are also established.

The novel Leal-polynomials for the multi-expansive approximation of nonlinear differential equations

This work presents the novel Leal-polynomials (LP) for the approximation of nonlinear differential equations of different kind. The main characteristic of LPs is that they satisfy multiple expansion points and its derivatives as a mechanism to replicate behaviour of the nonlinear problem, giving more accuracy within the region of interest. Therefore, the main contribution of this work is that LP satisfies the successive derivatives in some specific points, resulting more accurate polynomials than Taylor expansion does for the same degree of their respective polynomials. Such characteristic makes of LPs a handy and powerful tool to approximate different kind of differential equations including: singular problems, initial condition and boundary-valued problems, equations with discontinuities, coupled differential equations, high-order equations, among others. Additionally, we show how the process to obtain the polynomials is straightforward and simple to implement; generating a compact, and easy to compute, expression. Even more, we present the process to approximate Gelfand's equation, an equation of an isothermal reaction, a model for chronic myelogenous leukemia, Thomas-Fermi equation, and a high order nonlinear differential equations with discontinuities getting, as result, accurate, fast and compact approximate solutions. In addition, we present the computational convergence and error studies for LPs resulting convergent polynomials and error tendency to zero as the order of LPs increases for all study cases. Finally, a study of CPU time shows that LPs require a few nano-seconds to be evaluated, which makes them suitable for intensive computing applications.

Implementation of optimality criteria in the design of communication networks

We consider two frequently encountered problems in the modeling of the communication network, related to the construction of a graph of the communication network that meets certain conditions. Heuristic algorithms for solving these problems are proposed. The question of uniqueness of the solution of the set tasks is investigated. A positive result of solving the problem was obtained and sufficient conditions of uniqueness were found. The research and development of appropriate software are of practical importance in the design of real communication networks.

Optimization problem, arising in the development of high-dimensional communication networks, and some heuristic methods for solving them

We consider two frequently encountered problems in the simulation/modernization of the communication network related to the construction of a graph of the communication network that meets certain conditions. These problems concern the optimal topology of the communication network graph. The sum of the weights of the edges of the projected graph is considered as the target function. As restrictions-achievement by the indicator of stability of a communication network of some set threshold value. Heuristic algorithms for solving these problems are proposed. The question of uniqueness of the solution of the set tasks is investigated. A positive result of solving the problem was obtained and sufficient conditions of uniqueness were found. The research and development of appropriate software are of practical importance in the design of real communication networks.

Замкнутость бигармонической системы базисных потенциалов

The shift systems of the fundamental solution of biharmonic equation are considered. The shift sequence belongs to the complement of the bounded single-bond domain $Q$, so that all system functions satisfy the biharmonic equation in $Q$. The space of biharmonic functions $G_{2}(Q)$ is introduced as a closure in the $L_{2}(Q)$ norm of the linear shell of all kinds of shifts of the fundamental solution of biharmonic equation. The following problem is considered: what conditions the countable sequence of shifts must have so that the linear shell closure matches the entire $G _ {2} (Q) $ space, or, in other words, when is the considered system complete in $G _ {2} (Q)$? The problem for the harmonic case was considered by V.G. Lezhnev, he introduced a sufficient basis condition and proved the completeness and linear independence of shift systems of the fundamental solution of Laplace's equation.The work generalizes the basis condition to the biharmonic case and proves the closedness and linear independence of biharmonic system. The basis condition is related to the singularity condition of biharmonic functions. The proof relies on the property of continuity of potentials with a biharmonic nucleus and on the Rikier's boundary value problem solution.

Putative Receptors for Gravity Sensing in Mammalian Cells: The Effects of Microgravity

Gravity is a constitutive force that influences life on Earth. It is sensed and translated into biochemical stimuli through the so called “mechanosensors”, proteins able to change their molecular conformation in order to amplify external cues causing several intracellular responses. Mechanosensors are widely represented in the human body with important structures such as otholiths in hair cells of vestibular system and statoliths in plants. Moreover, they are also present in the bone, where mechanical cues can cause bone resorption or formation and in muscle in which mechanical stimuli can increase the sensibility for mechanical stretch. In this review, we discuss the role of mechanosensors in two different conditions: normogravity and microgravity, emphasizing their emerging role in microgravity. Microgravity is a singular condition in which many molecular changes occur, strictly connected with the modified gravity force and free fall of bodies. Here, we first summarize the most important mechanosensors involved in normogravity and microgravity. Subsequently, we propose muscle LIM protein (MLP) and sirtuins as new actors in mechanosensing and signaling transduction under microgravity.

Finite element Galerkin method for 2D Sobolev equations with Burgers’ type nonlinearity

In this article, the global existence of a unique strong solution to the 2D Sobolev equation with Burgers’ type nonlinearity is established using weak or weak* compactness type arguments. When the forcing function (f ≠ 0) is in L∞(L2), new a priori bounds are derived, which are valid uniformly in time as t↦∞ and with respect to the dispersion coefficient μ as μ↦0. It is further shown that the solution of the Sobolev equation converges to the solution of the 2D-Burgers’ equation with order O(μ). A finite element method is applied to approximate the solution in the spatial direction and the existence of a global attractor is derived for the semidiscrete scheme. Further, using a priori bounds and an integral operator, optimal error estimates are derived in L∞(L2)-norm, which hold uniformly with respect to μ as μ → 0. Since the constants in the error estimates have exponential growth in time, therefore, under a certain uniqueness condition, the error bounds are derived which are uniformly in time. More importantly, all the above results remain valid as μ tends to zero. Finally, this paper concludes with some numerical examples.

Competitive Coexistence in a Two-Strain Epidemic Model with a Periodic Infection Rate

In this article, we study the global dynamical behavior of a two-strain SIS model with a periodic infection rate. The positivity and boundedness of solutions are established, and the competitive exclusion conditions are given for the model. The conditions for the global stability of the disease-free equilibrium and persistence of the model are obtained. The conditions of coexistence in this model are also found. Finally, the conditions of uniqueness of the solution are proved.

On totally global solvability of controlled second kind operator equation

We consider the nonlinear evolutionary operator equation of the second kind as follows $\varphi=\mathcal{F}\bigl[f[u]\varphi\bigr]$, $\varphi\in W[0;T]\subset L_q\bigl([0;T];X\bigr)$, with Volterra type operators $\mathcal{F}\colon L_p\bigl([0;\tau];Y\bigr)\to W[0;T]$, $f[u]$: $W[0;T]\to L_p\bigl([0;T];Y\bigr)$ of the general form, a control $u\in\mathcal{D}$ and arbitrary Banach spaces $X$, $Y$. For this equation we prove theorems on solution uniqueness and sufficient conditions for totally (with respect to set $\mathcal{D}$) global solvability. Under natural hypotheses associated with pointwise in $t\in[0;T]$ estimates the conclusion on univalent totally global solvability is made provided global solvability for a comparison system which is some system of functional integral equations (it could be replaced by a system of equations of analogous type, and in some cases, of ordinary differential equations) with respect to unknown functions $[0;T]\to\mathbb{R}$. As an example we establish sufficient conditions of univalent totally global solvability for a controlled nonlinear nonstationary Navier-Stokes system.

A fractional order optimal 4D chaotic financial model with Mittag-Leffler law

In this paper, a fractional 4D chaotic financial model with optimal control is investigated. The fractional derivative used in this financial model is Atangana–Baleanu derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on Mittag-Leffler law. Optimal control is incorporated into the model to maximize output. The Adams–Moulton scheme of the Atangana–Baleanu derivative is utilized to obtain the numerical results which produce new attractors. Euler-Lagrange optimality conditions are determined for the fractional 4D chaotic financial model. The numerical results show that the memory factor has a great influences on the dynamics of the model.

Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminf _{tto T} Y(t) = xi = Y(T). Hence, we extend known results for a non-Markovian terminal condition.

On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty

AbstractWe revisit the linear Cournot model with uncertain demand that is studied in Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) and provide sufficient conditions for equilibrium uniqueness that complement the existing results. We show that if the distribution of the demand intercept has the decreasing mean residual demand (DMRD) or the increasing generalized failure rate (IGFR) property, then uniqueness of equilibrium is guaranteed. The DMRD condition implies log-concavity of the expected profits per unit of output without additional assumptions on the existence or the shape of the density of the demand intercept and, hence, answers in the affirmative the conjecture of Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) that such conditions may not be necessary.

Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences

Abstract Cournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order derivatives. Sufficient conditions for existence and uniqueness of the new model’s solution are obtained. The existence and local stability analysis of Nash equilibrium points along with other equilibrium points are examined. Some aspects of global stability analysis are treated. More significantly, the effects of seasonal periodic perturbations of parameters values are also explored. The multiscale fuzzy entropy measurements for complexity are employed for this case. Numerical simulations are presented in order to verify the analytical results. It is observed that the time-varying parameters induce very complicated dynamics in perturbed Cournot duopoly game compared with the unperturbed game.

Nonlocal boundary value problems for nonlinear toppled system of fractional differential equations

The aim of this paper is to study multiplicity results for the solutions of a coupled system of fractional differential equations. The problem under consideration is subjected to nonlocal boundary conditions involving Riemann-Liouville integrals and derivatives of fractional order. Necessary and sufficient conditions are established for the existence of at least one and more solutions by using various fixed point theorems of cone type. Moreover sufficient conditions for uniqueness is also discussed by using a concave type operator for the considered problem. Further, the conditions are also provided under which the considered system has no positive solution. The results are demonstrated by providing several examples.

A nonautonomous model for the effect of environmental toxins on plankton dynamics

The increasing input of environmental toxins in aquatic systems raises concerns regarding the environmental exposure and impact of toxins on natural aquatic environments. Phytoplankton and zooplankton appear to be among the most sensitive aquatic organisms to environmental toxins. Moreover, toxin-producing phytoplankton plays an important role in regulating the real aquatic ecosystems. In this paper, the combined effects of these factors on the dynamics of phytoplankton–zooplankton interactions are investigated. The phytoplankton grows logistically, but their growth rate is suppressed due to the presence of environmental toxins. The zooplankton is assumed to be generalist and follows logistic growth in the absence of phytoplankton. Also, it is considered that toxicants in the environment are increased constantly due to different natural and human behaviors. Global sensitivity analysis helps to identify the most significant parameters that reduce the environmental toxins in the system. Among these, the input rate of environmental toxins, contact rate between phytoplankton and environmental toxins, and environmental toxins-induced growth suppression of phytoplankton have destabilizing effect on the dynamics of system, while the depletion rate of environmental toxins has stabilizing effect. Therefore, it is imperative to modulate the depletion rate of environmental toxins to prevent the crash of the aquatic food web system. Further, we incorporate seasonal variations in the model, letting the parameters become functions of time. Sufficient conditions for the existence and stability of positive periodic solutions are obtained. We also derive conditions for existence, uniqueness and stability of a positive almost periodic solution. Large values of time-dependent toxin release by phytoplankton and input rate of environmental toxins induce periodic solutions of the nonautonomous system while the corresponding autonomous system exhibits a stable focus. Interestingly, our nonautonomous system exhibits bursting patterns for two slow rationally related excitation frequencies. Finally, we convert our deterministic autonomous model into stochastic model by introducing additive noise term. We find that the stability of the system gets disturbed in the presence of environmental fluctuation.

Subject–verb agreement dependency in Turkish Broca’s aphasia: impairments in event occurrence and consequences for discourse-linking

ABSTRACT Background: Inflecting the verb for agreement requires an intact discourse-semantic ability in addition to that for morphosyntax, since the use of person involves a link between the participants in the speech act and the morphosyntactic expression of this feature. Unlike the first person (the Speaker), the second person (the Addressee) requires additional discourse processing, termed “discourse-linking”. Individuals with Broca’s aphasia may have impaired discourse-linking, which may affect their ability to process second person pronouns and produce verb morphology for the second person. Aims: This study investigated whether the discourse-linking involved in processing second person pronouns contributes to sentence production deficits in Broca’s aphasia. Methods & Procedures: The sample consisted of 16 Turkish individuals with Broca’s aphasia (mean age: 54.8 years; SD: 14.0) who were matched in age with a control group of 16 neurologically intact Turkish individuals (mean age: 54.9; SD: 13.1). Each group completed a language task with first and second person singular or plural agreement conditions. Target agreement morphology was elicited using sentence-initial first and second person singular or plural pronouns. The plural (reference to a group) has a more complex discourse-representation than the singular (reference to an individual). Outcomes & Results: The group of individuals with Broca’s aphasia showed the following production hierarchy: first person singular (highest accuracy rate) > first person plural > second person singular > second person plural (lowest accuracy rate). There was no discrepancy between test conditions for the control group. Conclusions: The discourse-linking involved in processing second person pronouns contributes to sentence production deficits and this deficit is exacerbated by plurality in Broca’s aphasia. We suggest that cognitive-semantic intervention which focusses on the broader underlying impairment in deciphering event occurrence features (participant-time-location) could improve the use of the second person and other discourse-linked constructions (e.g., past time reference, object pronouns) which are selectively affected in Broca’s aphasia.

Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

ABSTRACTWe obtain exact necessary and sufficient conditions for existence and uniqueness of solutions of a class of homothetic recursive utility models postulated by Epstein and Zin. The conditions center on a single test value with a natural economic interpretation. The test sheds light on the relationship between valuation of cash flows, impatience, risk adjustment, and intertemporal substitution of consumption. We propose two methods to compute the test value when an analytical solution is not available. We further provide several applications.

Endpoint Estimates of Commutators of Singular Integrals vs. Conditions on the Symbol

Endpoint estimates of commutators $$T_b$$ of singular integrals T, are studied over general spaces that include, in particular, BMO and Lipschitz spaces. We also characterize the conditions of the symbol b in order to obtain the boundedness of the commutators of all Riesz transforms between these spaces. Finally, we apply these results over several interesting known spaces.

Contradictory Postulates of Singularity

Modification of rigid body angular momentum permits controlled rotational maneuvers, and one common momentum-exchange actuator contains challenging mathematical singularities that occur when the actuator geometrically aligns perpendicularly to the commanded torque direction. Substantial research has arisen toward singularity avoidance, singularity escape (when avoidance fails), and singularity penetration which permits safe flight through regions of singularity. The latter two in particular, singularity escape and penetration require mathematical calculations of singular and near-singular quantities (very large numbers) using constituent numbers that are sometimes very small. This dichotomy leads to interesting peculiarities in some specific geometries. This short communication critically evaluates three often spoke postulates for defining singularity and the axioms that accompany the postulates. Researchers using disparate postulates arrive at contradictory conclusions about singularities, and we examine these peculiarities, leading to a few conclusions. Singular conditions must never be declared in the abstract without consideration for the commanded maneuver (e.g. the claim “the CMG system is singular”). Seeking the true angular momentum capability at near-planar skew angles, this research concludes that performance prediction is difficult installations at low skew angles should be avoided whenever permissible to enhance abilities of mathematical calculations. It will be shown that maximum momentum performance is easily predicted at very high and very low skew angles, and performance will be shown to be lowest at mid-values of skew angle. Meanwhile, maximum singularity-free performance remains elusive at even modestly low skew-angles.

Hybrid‐Trefftz stress elements for plate bending

SummaryThe hybrid‐Trefftz stress element is used to emulate conventional finite elements for analysis of Kirchhoff and Mindlin‐Reissner plate bending problems. The element is hybrid because it is based on the independent approximation of the stress‐resultant and boundary displacement fields. The Trefftz variant is consequent on the use of the formal solutions of the governing Lagrange equation to approximate the stress‐resultant field. In order to emulate conventional elements, nodal functions are used to approximate the displacements on the boundary of the element. Duality is used to set up the element solving system. The associated variational statements and conditions for existence and uniqueness of solutions are recovered. Triangular and quadrilateral elements are tested and characterized in terms of convergence, sensitivity to shear‐locking, and shape distortion. Their relative performance is assessed using assumed strain Mixed Interpolation of Tensorial Components (MITC) elements and recently proposed Trefftz‐based elements. This relative assessment is extended to a hypersingular problem to illustrate the effect of enriching the domain and boundary approximation bases.