The Median Principle for Inequalities and Applications

The median principle is applied for different integral inequalities of Gruss and Ostrowski type

Generalisation of a Waiting-Time Relation

AbstractA generalisation of a waiting-time relation is developed by the use of Laplace transform theory. The generalisation produces an infinite series and it is demonstrated how it may be summed by representation in closed form. Extensions and examples of the waiting-time relation are given

New bounds for the Čebyšev functional

AbstractIn this paper some new inequalities for the Čebyšev functional are presented. They have applications in a variety of branches of applied mathematics

Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided

Norm Estimates for the Difference Between Bochner's Integral and the Convex Combination of Function's Values

Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a,b]

On inequalities of Jensen-Ostrowski type

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of (Formula Presented), with various assumptions on the absolutely continuous function f:[a,b]→C and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting λ=0 and ζ=∫Ωgdμ, respectively. In particular, we obtain some bounds for the discrepancy in Jensen’s integral inequality. Applications of these inequalities for f-divergence measures are also given

Data consistency in transactional storage systems: a centralised approach.

We introduce an interleaving operational semantics for describing the client-observable behaviour of atomic transactions on distributed key-value stores. Our semantics builds on abstract states comprising centralised, global key-value stores and partial client views. We provide operational definitions of consistency models for our key-value stores which are shown to be equivalent to the well-known declarative definitions of consistency model for execution graphs. We explore two immediate applications of our semantics: specific protocols of geo-replicated databases (e.g. COPS) and partitioned databases (e.g. Clock-SI) can be shown to be correct for a specific consistency model by embedding them in our centralised semantics; programs can be directly shown to have invariant properties such as robustness results against a weak consistency model

Specifying and Verifying Concurrent Algorithms with Histories and Subjectivity

We present a lightweight approach to Hoare-style specifications for fine-grained concurrency, based on a notion of time-stamped histories that abstractly capture atomic changes in the program state. Our key observation is that histories form a partial commutative monoid, a structure fundamental for representation of concurrent resources. This insight provides us with a unifying mechanism that allows us to treat histories just like heaps in separation logic. For example, both are subject to the same assertion logic and inference rules (e.g., the frame rule). Moreover, the notion of ownership transfer, which usually applies to heaps, has an equivalent in histories. It can be used to formally represent helping---an important design pattern for concurrent algorithms whereby one thread can execute code on behalf of another. Specifications in terms of histories naturally abstract granularity, in the sense that sophisticated fine-grained algorithms can be given the same specifications as their simplified coarse-grained counterparts, making them equally convenient for client-side reasoning. We illustrate our approach on a number of examples and validate all of them in Coq.Comment: 17 page

An Ostrowski type inequality for double integrals in terms of LpL_p-norms and applications in numerical integration

An inequality of the Ostrowski type for double integrals and applications in Numerical Analysis in connection with cubature formulae are given