We provide two methods to construct zero-range processes with superlinear rates on Zd. In the first method these can grow very fast, if either dynamics and initial distribution are translation invariant or only nearest neighbour jumps permitted, in one-dimensional lattice. second cannot as fast but more general allowed.

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value ind...

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...

APPLIED MATHEMATICS Correction for ‘‘On the behavior of a capillary surface in a wedge,’’ by Paul Concus and Robert Finn, which appeared in issue 2, June 1, 1969, of Proc Natl Acad Sci USA (63:292–299). Owing to a printer’s error, the initial sentence of the abstract appeared as ‘‘Estimates above and below are obtained for the height of the equilibrium-free surface of a liquid’’ rather than the...

Hash Proof Systems or Smooth Projective Hash Functions (SPHFs) are a form of implicit arguments introduced by Cramer and Shoup at Eurocrypt’02. They have found many applications since then, in particular for authenticated key exchange or honest-verifier zero-knowledge proofs. While they are relatively well understood in group settings, they seem painful to construct directly in the lattice sett...

We consider the adversarial combinatorial multi-armed bandit (CMAB) problem, whose decisionset can be exponentially large with respect to the number of given arms. To avoid dealing with suchlarge decision sets directly, we propose an algorithm performed on a zero-suppressed binary decisiondiagram (ZDD), which is a compressed representation of the decision set. The proposed algor...

τ∗ = inf { t ∈ [0, T ] | B t ≤ b−(t) or B t ≥ b+(t) } where the function t 7→ b−(t) is continuous and increasing on [0, T ] with b−(T ) = 0 , the function t 7→ b+(t) is continuous and decreasing on [0, T ] with b+(T ) = 0 , and the pair b− and b+ can be characterised as the unique solution to a coupled system of nonlinear Volterra integral equations. This also yields an explicit formula for V∗ ...

Total joint arthroplasty is a successful and recently developed procedure performed on an increasing number of patients. However, periprosthetic joint infection (PJI) is a calamitous complication of this operation, the incidence of which is 1-2%. Different investigators have defined numerous definitions for this complication, but the Musculoskeletal Infection Society (MSIS) definition of PJI ha...

John Hemmerling, a senior in chemical engineering and project leader, Jeremy Pan, a sophomore in computer science, and Sahil Bhalla and Karan Kedia, both freshman in fi rst-year engineering, are a team of four students participating in the Engineering Projects in Community Service (EPICS) Environmental Improvement Initiatives (EII). In this article they describe how they are investigating waste...