THERMODYNAMIC FORMALISM FOR SUBADDITIVE SEQUENCE OF DISCONTINUOUS FUNCTIONS

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.

Functional inorganic additives in composite solid-state electrolytes for flexible lithium metal batteries

Flexible lithium metal batteries with high capacity and power density have been regarded as the core power resources of wearable electronics.However,the main challenge lies in the limited electrochemical performance of solid-state polymer electrolytes,which hinders further practical applications.Incorporating functional inorganic additives is an effective approach to improve the performance,including increasing ionic conductivity,achieving dendrite inhibiting capability,and improving safety and stability.Herein,this review summarizes the latest developments of functional inorganic additives in composite solid-state electrolytes for flexible metal batteries with special emphasis on their mechanisms,strategies,and cutting-edge applications,in particular,the relationship between them is discussed in detail.Finally,the perspective on future research directions and the key challenges on this topic are outlooked.

Stability analysis of approximately multidimensional additive mappings on fuzzy spaces

The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.

Functional additives for solid polymer electrolytes in flexible and high-energy-density solid-state lithium-ion batteries

Solid polymer electrolytes(SPEs)have become increasingly attractive in solid-state lithium-ion batteries(SSLIBs)in recent years because of their inherent properties of flexibility,processability,and interfacial compatibility.However,the commercialization of SPEs remains challenging for flexible and high-energy-density LIBs.The incorporation of functional additives into SPEs could significantly improve the electrochemical and mechanical properties of SPEs and has created some historical milestones in boosting the development of SPEs.In this study,we review the roles of additives in SPEs,highlighting the working mechanisms and functionalities of the additives.The additives could afford significant advantages in boosting ionic conductivity,increasing ion transference number,improving high-voltage stability,enhancing mechanical strength,inhibiting lithium dendrite,and reducing flammability.Moreover,the application of functional additives in high-voltage cathodes,lithium-sulfur batteries,and flexible lithiumion batteries is summarized.Finally,future research perspectives are proposed to overcome the unresolved technical hurdles and critical issues in additives of SPEs,such as facile fabrication process,interfacial compatibility,investigation of the working mechanism,and special functionalities.

APPROXIMATION OF A CAUCHY-JENSEN ADDITIVE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.

RANDOM APPROXIMATION OF AN ADDITIVE FUNCTIONAL EQUATION OF m-APPOLLONIUS TYPE

In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原

Adhesive hydrogels in osteoarthritis:from design to application

Osteoarthritis(OA)is the most common type of degenerative joint disease which affects 7%of the global population and more than 500 million people worldwide.One research frontier is the development of hydrogels for OA treatment,which operate either as functional scaffolds of tissue engineering or as delivery vehicles of functional additives.Both approaches address the big challenge:establishing stable integration of such delivery systems or implants.Adhesive hydrogels provide possible solutions to this challenge.However,few studies have described the current advances in using adhesive hydrogel for OA treatment.This review summarizes the commonly used hydrogels with their adhesion mechanisms and components.Additionally,recognizing that OA is a complex disease involving different biological mechanisms,the bioactive therapeutic strategies are also presented.By presenting the adhesive hydrogels in an interdisciplinary way,including both the fields of chemistry and biology,this review will attempt to provide a comprehensive insight for designing novel bioadhesive systems for OA therapy.

Ultra High Early Strength Self-compacting Mortar Based on Sulfoaluminate Cement and Silica Fume

The influences of silica fume and aluminum sulfate on hydration process of sulfoaluminate cement were carried out by ring flow, setting time, hydration heat, XRD and DTG analyses. In addition, mortar mixtures with different functional additives have been studied through compressive strength, flexural strength, volume stability at early age and porosity characterization tests. The results show that the addition of silica fume and aluminum sulfate reduces the fluidity and shortens the setting time of sulfoaluminate cement paste, promoting hydration process and increasing hydration products at early age. In the case of appropriate proportion of mortar, the inclusion of hydroxy propyl methyl cellulose, dispersible polypropylene fiber arid organic silicon kind of defoamer can control segregation and bleeding, improve mechanical strength and volume stability at early age, and modify the pore distribution of sulfoaluminate cement mortar, respectively. The sulfoaluminate cement mortar can carry out gravitational grouting in the absence of outside force, the compressive strength of 2 hours and 24 hours have reached 26 and 58 MPa respectively, and have good micro- expansion and tiny.pore distribution characterization.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.

Some Properties of Conditioned Superdiffusion

Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.

NOTES ON ERDOS' CONJECTURE

Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent, it is both sufficient and necessary that there exist three numbers X0 and X1 < X2 such that limsup(FN(X2) - FN(X1)) > 0 holds, and Lo = N→ ∞ lim FN(X0) exists. Moreover, the authors point out that they can also obtain the same result in the weakened case of lim inf P(Xn = 0) > 0.

Square Root Functional Equation on Positive Cones

A square root functional equation on positive cones of C＇-algebras is introduced and its solution and Hyers-Ulam-Rassias stability are investigated.

Designing Advanced Liquid Electrolytes for Alkali Metal Batteries:Principles,Progress,and Perspectives

The ever-growing pursuit of high energy density batteries has triggered extensive efforts toward developing alkali metal(Li,Na,and K)battery(AMB)technologies owing to high theoretical capacities and low redox potentials of metallic anodes.Typically,for new battery systems,the electrolyte design is critical for realizing the battery electrochemistry of AMBs.Conventional electrolytes in alkali ion batteries are generally unsuitable for sustaining the stability owing to the hyper-reactivity and dendritic growth of alkali metals.In this review,we begin with the fundamentals of AMB electrolytes.Recent advancements in concentrated and fluorinated electrolytes,as well as functional electrolyte additives for boosting the stability of Li metal batteries,are summarized and discussed with a special focus on structure-composition-performance relationships.We then delve into the electrolyte formulations for Na-and K metal batteries,including those in which Na/K do not adhere to the Li-inherited paradigms.Finally,the challenges and the future research needs in advanced electrolytes for AMB are highlighted.This comprehensive review sheds light on the principles for the rational design of promising electrolytes and offers new inspirations for developing stable AMBs with high performance.

Ruzsa's Constant on Additive Functions

A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved that there exists a constant c such that for any additive function f, μ（x） ≤ cv（x^2） ＋ cf, where cf is a constant depending only on f. Denote by Raf the least such constant c. We cMl Raf Ruzsa＇s constant on additive functions. In this paper, we prove that Raf≤ 20.

On Sectional Cycles in Translation Quivers

In this paper, we prove that there exists no sectional cycle in a translation quiver under certain conditions. So, we generalize Dautista and Smalφ's corresponding result on AR-quiver of an artin algebra.

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.

A Generalized Cubic Functional Equation

In this paper, we determine the general solution of the functional equation f1 （2x ＋ y） ＋ f2（2x - y） = f3（x ＋ y） ＋ f4（x - y） ＋ f5（x） without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 ： R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f（2x ＋ y） ＋ f（2x - y） = g（x ＋ y） ＋ g（x - y） ＋ h（x） and f（2x ＋ y） - f（2x - y） = g（x ＋ y） - g（x - y）. The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi.

ADDITIVE FUNCTIONALS AND PERTURBATION OF SEMIGROUP

The perturbation of semigroup by a multiplicative functional with bounded variation is investigated in the frame of weak duality. The strong continuity and Schrodinger type equation of the perturbated semigroup are discussed. A few switching identities and formulae conerning dual additive functionals and Revuz measures are given.

Pricing and Inventory Control Strategy for a Periodic-Review Energy Buy-Back System

Along with the rapid development of economics and enhancement of industrialization, the power demand keeps rising and frequently creates mismatch between demand and supply in electricity.This provides miscellaneous energy buy-back programs with great opportunities. Such programs, when activated, offer certain amount of financial compensations to participants for reducing their energy consumption during peak time. They aim at encouraging participants to shift their electricity usage from peak to non-peak time, and thereby release the demand pressure during peak time. This paper considers a periodic-review joint pricing and inventory decision model under an energy buy-back program over finite planning horizons, in which the compensation levels, setup cost and additive random demand function are incorporated. The objective is to maximize a manufacturer's expected total profit.By using Veinott's conditions, it is shown that the manufacturer's optimal decision is a state dependent(s, S, P) policy under a peak market condition, or partly an(s, S, A, P) policy under the normal market condition.