Sufficient Conditions In Order Research Articles

Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions

Two hypotheses on the class $${\mathcal {L}}(\gamma )$$ in the class $$\mathcal {OS}\cap \mathcal {ID}$$ are discussed. Two weak hypotheses on the class $${\mathcal {L}}(\gamma )$$ in the class $$\mathcal {OS}\cap \mathcal {ID}$$ are proved. A necessary and sufficient condition in order that, for every $$t>0$$ , the t-th convolution power of a distribution in the class $$\mathcal {OS}\cap \mathcal {ID}$$ belongs to the class $${\mathcal {L}}(\gamma )$$ is given. Sufficient conditions are given for the validity of two hypotheses on the class $${\mathcal {L}}(\gamma )$$ .

Variable exponent Lebesgue spaces which are not Riesz isomorphic to their own square

Classical Lebesgue $$L^p$$-spaces, $$1\le p\le \infty $$, are Riesz isomorphic to their own square. If p(t), $$t\in (0,1)$$, is a bounded diffeomorphism, then the variable exponent Lebesgue space $$L^{p(\cdot )}(\Omega )$$ is not Riesz isomorphic to its own square. We give sufficient conditions in order to avoid this situation.

Projectively coresolved Gorenstein flat and ding projective modules

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, (respectively that of projectively coresolved Gorenstein flat modules, ), to coincide with the class of Ding projective modules ( We show that if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have We also show that over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have where is the class of Gorenstein projective modules.

The combined effect of optimal control and swarm intelligence on optimization of cancer chemotherapy

Background and Objectives: In cancer therapy optimization, an optimal amount of drug is determined to not only reduce the tumor size but also to maintain the level of chemo toxicity in the patient's body. The increase in the number of objectives and constraints further burdens the optimization problem. The objective of the present work is to solve a Constrained Multi- Objective Optimization Problem (CMOOP) of the Cancer-Chemotherapy. This optimization results in optimal drug schedule through the minimization of the tumor size and the drug concentration by ensuring the patient's health level during dosing within an acceptable level.Methods: This paper presents two hybrid methodologies that combines optimal control theory with multi-objective swarm and evolutionary algorithms and compares the performance of these methodologies with multi-objective swarm intelligence algorithms such as MOEAD, MODE, MOPSO and M-MOPSO. The hybrid and conventional methodologies are compared by addressing CMOOP.Results: The minimized tumor and drug concentration results obtained by the hybrid methodologies demonstrate that they are not only superior to pure swarm intelligence or evolutionary algorithm methodologies but also consumes far less computational time. Further, Second Order Sufficient Condition (SSC) is also used to verify and validate the optimality condition of the constrained multi-objective problem.Conclusion: The proposed methodologies reduce chemo-medicine administration while maintaining effective tumor killing. This will be helpful for oncologist to discover and find the optimum dose schedule of the chemotherapy that reduces the tumor cells while maintaining the patients’ health at a safe level.

Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric

The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant . Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.

Penalization of Dirichlet Boundary Control for Nonstationary Magneto-Hydrodynamics

Penalization of Dirichlet boundary controlled nonstationary magneto-hydrodynamic equations is considered. Asymptotic behavior of solutions of a penalized control problem with respect to the penalty parameter is investigated. It is proved that solutions of the penalized boundary control problem converge to the solutions of the Dirichlet control problem as penalty parameter $\epsilon$ goes to zero. The existence of optimal solutions as well as the characterization of such solutions by first order necessary conditions are established. A second order sufficient optimality condition for the optimal control problem is also developed. Numerical results are provided showing the feasibility and effectiveness of the penalty method.

Critical Cones for Sufficient Second Order Conditions in PDE Constrained Optimization

In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a Tikhonov regularization term. Unlike finite dimensional optimization or control problems involving Tikhonov regularization, second order sufficient optimality conditions for the control problems we deal with must be imposed in a cone larger than the one used to obtain necessary conditions. Different extensions of this cone have been proposed in the literature for different kinds of minima: strong or weak minimizers for optimal control problems. After a discussion on these extensions, we propose a new extended cone smaller than those considered until now. We prove that a second order condition based on this new cone is sufficient for a strong local minimum.

A study of convergences in partially ordered sets

In this paper we obtain alternative proofs of the fact that the ideal-o2-convergence in a poset is topological if and only if the poset is O2-doubly continuous. We also introduce and study the ideal-lim-inf-convergence in a poset, exploiting the relation between the induced ideal-lim-inf-topology, lim-inf-topology and Scott topology. Finally, we give a necessary and sufficient condition in order the ideal-lim-inf-convergence to be topological.

An Augmented Lagrangian based Semismooth Newton Method for a Class of Bilinear Programming Problems

This paper proposes a semismooth Newton method for a class of bilinear programming problems (BLPs) based on the augmented Lagrangian, in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers. Without strict complementarity, the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition. At last, numerical results are reported to show the performance of the proposed method.

Atomic sublattices and basic derivatives in finance

Suppose that E is a vector lattice where the ordering and the lattice operations in E are defined pointwise by a countable family $${\mathcal {F}}=\{f_i|i\in {{\mathbf {N}}}\}$$ of positive linear functional of E and Z is a sublattice of E. Based on algebraic and order properties of E we give necessary and sufficient conditions in order Z to be atomic. Especially we show the existence of a basic sequence $$\{b_n\}$$ of extremal points (atoms) of $$Z_+$$ so that for any $$x\in Z_+$$ a unique sequence $$({\widehat{x}}(n))$$ of real components of x with respect to $$\{b_n\}$$ exists so that $$x=\sup \{{\widehat{x}}(n)b_n\;|\;n\in {{\mathbf {N}}}\}$$ and also $$x=sup_{n}\sum _{i=1}^n{\widehat{x}}(i)b_i$$ . These results give an answer to the problem of the existence of basic derivatives in financial markets.

Energy-dissipation balance of a smooth moving crack

In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [10] valid for straight fractures.

HVAC-Based Cooperative Algorithms for Demand Side Management in a Microgrid

The high penetration of renewable power generators and various loads have brought a great challenge for dispatching energy in a microgrid system. Heating ventilation air conditioning (HVAC) system, as a household appliance with high popularity, can be considered as an effective technology to alleviate energy dispatch issues. This paper presents novel distributed algorithms based on HVAC to solve the demand side management problem, where the microgrid system with HVAC units is considered as a multi-agent system (MAS). The approach provides a desirable operating frequency signal for each HVAC based on the power mismatch value occurring on each local bus. It utilizes demand response of the HVAC units to minimize the supply-demand mismatch, thus reducing the quantity and capacity of energy storage devices potentially to be required. Compared with existing approaches focusing on the distributed algorithms under a fixed communication network, this paper addresses a consensus problem under a switching topology by using the Lyapunov argument. It is verified that a jointly strong and connected topology is a sufficient condition in order to achieve an average consensus for a time-varying topology. A number of cases are studied to evaluate the effectiveness of the algorithms by taking into account its power constraints, dynamic behaviors, anti-damage characteristics and time-varying communication topology. Modelling these system interactions has demonstrated the feasibility of the proposed microgrid system.

Some completely semisimple HNN-extensions of inverse semigroups

We give necessary and sufficient conditions in order that lower bounded HNN-extensions of inverse semigroups and HNN-extensions of finite inverse semigroups are completely semisimple semigroups. Since it is well known that an inverse semigroup is completely semisimple if and only if it does not contain a copy of the bicyclic semigroup, we first characterize such HNN-extensions containing a bicyclic subsemigroup making use of the special feature of their Schützenberger automata.

Positive periodic solutions for Lotka–Volterra systems with a general attack rate

The paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel’skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the functional response of predators are discussed.

Coordinated Freight Routing With Individual Incentives for Participation

The sharp increase in e-commerce over the last few years has led to an increase in the volume of trucks both in ports and in commercial areas. Truck traffic has a negative impact on traffic flow in general due to the size of trucks and their slower dynamics. The continuously increasing use of navigation apps has led drivers to make their routing decisions in an independent manner in an effort to minimize their own individual travel time, with possible significant deviation from a socially optimum solution. In this paper, we consider the use of coordinated routing in order to achieve load balancing. Users send their OD matrices as well as their preferred departure time to the coordinator who gives them routing instructions based on a socially optimum cost. This design enables us to derive sufficient conditions under which we prove the existence of mechanisms which are truthful in equilibrium, budget balanced on average and create individual incentives for voluntary participation of the truck drivers. Subsequently, we design our mechanism in a way that only uses a minimal set of sufficient conditions in order to guarantee the existence of a solution and maximize its efficiency. Finally, the extensive simulation results of our approach in the Braess and the Sioux Falls networks demonstrate that the proposed mechanism can approach the system optimum solution.

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. We have also obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. We have also calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding Kählerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to some subgroup of the homothetic group of the coresponding local Kählerian metric.

Effect of machine stiffness on interpreting contact force–indentation depth curves in adhesive elastic contact experiments

Dry adhesion plays a critical role in many fields, including the locomotion of some insects and failure of microelectromechanical systems. The Dupré’s work of adhesion of a contact interface is an important metric of dry adhesion. It is often measured by applying the Johnson–Kendall–Roberts (JKR) theory [1] to contact force–indentation depth curves that are measured using an atomic force microscope (AFM), or an instrument modeled after it. The JKR theory has been exceptionally successful in interpreting contact force–indentation depth measurements and explaining adhesive, elastic contact phenomena, such as the pull-in and pull-off instabilities. However, in many cases the JKR theory predicts a lower magnitude for the pull-off force than what is experimentally measured, and it does not capture the finite changes in the indentation depth that occur during the pull-in and pull-off instabilities. In those cases, applying the JKR theory to calculate the work of adhesion from only the measured pull-off force is likely to give highly inaccurate results. We believe that these discrepancies occur because the classical JKR theory ignores the machine stiffness—which, in the case of AFM-type instruments, is the stiffness of the mechanical structure that connects the tip to the translation stage, which moves the tip towards and away from the substrate. In this paper, we present a model that is related to, but more general than, the JKR theory that accounts for the machine stiffness. This model explains the experimental data better than the JKR theory in the cases where the JKR theory displays the aforementioned discrepancies. We consider both the first order necessary and the higher order sufficiency conditions while deriving the solutions in our model.

An integral type characterization of Lipschitz functions over metric-measure spaces

The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be essentially Lipschitzian.

Tridiagonal M-matrices whose inverse is tridiagonal and related pentadiagonal matrices

A necessary and sufficient condition in order to guarantee that the inverse of a tridiagonal M-matrix is tridiagonal is provided. Pentadiagonal M-matrices whose inverse is pentadiagonal are also analyzed.

Wronskians of Fourier and Laplace transforms

Associated with a given suitable function, or a measure, on R \mathbb {R} , we introduce a correlation function so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation function, and the same holds for the Laplace transform. We obtain two types of results. First, we show that Wronskians of the Fourier transform of a nonnegative function on R \mathbb {R} are positive definite functions and that the Wronskians of the Laplace transform of a nonnegative function on R + \mathbb {R}_+ are completely monotone functions. Then we establish necessary and sufficient conditions in order that a real entire function, defined as a Fourier transform of a positive kernel K K , belongs to the Laguerre–Pólya class, which answers an old question of Pólya. The characterization is given in terms of a density property of the correlation kernel related to K K , via classical results of Laguerre and Jensen and employing Wiener’s L 1 L^1 Tauberian theorem. As a consequence, we provide a necessary and sufficient condition for the Riemann hypothesis in terms of a density of the translations of the correlation function related to the Riemann ξ \xi -function.