Partial or Truncated Sharing Values of Meromorphic Functions with Their Shifts

We mainly study the periodicity theorems of meromorphic functions having truncated or partial sharing values with their shifts, where meromorphic functions are of hyper order less than 1 and N（r, f） aT（r; f） for some positive number a.

Unicity Theorems of Mesomorphic Functions with Three Weighted Sharing Values

In this paper,with the idea of weighted sharing values,we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values.We obtain some theorems which improve the results of H X Yi and W R L.

ON THE SHARING VALUES OF ALGEBROID FUNCTIONS AND THEIR DERIVATIVES

In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.

On meromorphic functions sharing one value

The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.

Entire functions sharing a value with its weight

A uniqueness theorem for entire functions sharing one finite complex value with weight two is proved by using Nevanlinna theory , and this improves the result of Fang and Hua.

UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE

We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].

The Expression of Slow-growing Meromorphic Functions Sharing One Value CM with Their Derivatives

In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with their derivatives by a new method. Our main result is the supplementary of a related result due to Li and Yi(Li X M, Yi H X. Uniqueness of meromorphic functions sharing a meromorphic function of a small order with their derivatives. Ann. Polon. Math., 2010, 98(3):201–219).

A Trust Value Sharing Scheme in Heterogeneous Identity Federation Topologies

Recent developments in heterogeneous identity federation systems have heightened the need for the related trust management system.The trust management system evaluates,manages,and shares users’trust values.The service provider(SP)members of the federation system rely on users’trust values to determine which type and quality of service will be provided to the users.While identity federation systems have the potential to help federated users save time and energy and improve service experience,the benefits also come with significant privacy risks.So far,there has been little discussion about the privacy protection of users in heterogeneous identity federation systems.In this paper,we propose a trust value sharing scheme based on a proxy ring signature for the trust management system in heterogeneous identity federation topologies.The ring signature schemes can ensure the validity of the data and hide the original signer,thereby protecting privacy.Moreover,no group manager participating in the ring signature,which naturally matches with our decentralized heterogeneous identity federation topologies.The proxy signature can reduce the workload of the private key owner.The proposed scheme shortens the calculation time for verifying the signature and then reduces the overall time consumption in the process of trust sharing.Our studies prove that the proposed scheme is privacy-preserving,efficient,and effective.

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k ＋ 12. If f^n＋ af^（k）and g^n＋ ag^（k）share b CM and the b-points of f^n＋ af^（k）are not the zeros of f and g, then f and g are either equal or closely related.

Curating Spaces of Hope: Coproducing Shared Values in Uncertain Times

This paper sets out a new paradigm of faith based organisation(FBO)called Curating Spaces of Hope.The paper sets out the paradigm and the interdisciplinary literatures into which the paradigm is applied namely,the diversifying belief landscape in the UK,the postsecular,the redefinition of FBOs,and liminality as the new norm in policy.The paper then turns to ethnographic research to evidence the ability of the paradigm to map and coproduce shared values,before considering applications of Curating Spaces of Hope in post-pandemic contexts in the north west of England through case studies with ecumenical Christian,non-religious,and Turkish Muslim and interfaith contexts.

Meromorphic Functions Sharing Two Values

Let f and g be two nonconstant meromorphic functions,and n be a positive integer.If f^(n)(z)and g^(n)(z)share 1 CM(counting multiplicities),f(z)and g(z)share∞IM(ignoring multiplicities),and N(r,1f)+N(r,1g)=S(r,f)+S(r,g),then either f(z)≡tg(z)or f(z)g(z)≡t,where t^(n)=1.As an application,shared values problems of a meromorphic function related to its shifts and difference operators are also investigated.

Consumers'privacy data sharing between the seller and the e-commerce platform

Due to the fact that consumers'privacy data sharing has multifaceted and complex effects on the e-commerce platform and its two sided agents,consumers and sellers,a game-theoretic model in a monopoly e-market is set up to study the equilibrium strategies of the three agents(the platform,the seller on it and consumers)under privacy data sharing.Equilibrium decisions show that after sharing consumers'privacy data once,the platform can collect more privacy data from consumers.Meanwhile,privacy data sharing pushes the seller to reduce the product price.Moreover,the platform will increase the transaction fee if the privacy data sharing value is high.It is also indicated that privacy data sharing always benefits consumers and the seller.However,the platform's profit decreases if the privacy data sharing value is low and the privacy data sharing level is high.Finally,an extended model considering an incomplete information game among the agents is discussed.The results show that both the platform and the seller cannot obtain a high profit from privacy data sharing.Factors including the seller's possibility to buy privacy data,the privacy data sharing value and privacy data sharing level affect the two agents'payoffs.If the platform wishes to benefit from privacy data sharing,it should increase the possibility of the seller to buy privacy data or increase the privacy data sharing value.

Complex and p-Adic Meromorphic Functions f′P′( f ),g′P′(g) Sharing a Small Function

Let K be a complete algebraically closed p-adic field of characteristic zero. We apply results in algebraic geometry and a new Nevanlinna theorem for p-adic meromorphic functions in order to prove results of uniqueness in value sharing prob-lems, both on K and on C. Let P be a polynomial of uniqueness for meromorphic functions in K or C or in an open disk. Let f , g be two transcendental meromorphic functions in the whole field K or in C or meromorphic functions in an open disk of K that are not quotients of bounded analytic functions. We show that if f′P′（ f ） and g′P′（g） share a small function α counting multiplicity, then f=g, provided that the multiplicity order of zeros of P′satisfy certain inequalities. A breakthrough in this pa-per consists of replacing inequalities n≥k＋2 or n≥k＋3 used in previous papers by Hypothesis （G）. In the p-adic context, another consists of giving a lower bound for a sum of q counting functions of zeros with （q-1） times the characteristic function of the considered meromorphic function.

Uniqueness of Meromorphic Functions Sharing One Set

In this paper,we study uniqueness of meromorphic functions sharing one set,and obtain some results,which improve and extend the original results.

NORMAL FAMILIES AND SHARED VALUES OF HOLOMORPHIC FUNCTIONS

Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.

NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES

We obtain some normality criteria of families of meromorphic functions sharing values related to Hayman conjecture, which improves some earlier related results.

ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS

In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.

BOREL'S DIRECTIONS AND SHARED VALUES

In this article, we study the problems of Borel＇s directions of meromorphic func- tions concerning shared values and prove that if two meromorphie functions of infinite order share three distinct values, their Borel＇s directions are same.

UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN

In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].

Uniqueness Problems for Meromorphic Functions that Share Three Values

This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.