Related papers: Classes of Gap Balancing Numbers
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…
For $p\geq 1$ one can define a generalization of the unknotting number $tu_p$ called the $p$th untwisting number which counts the number of null-homologous twists on at most $2p$ strands required to convert the knot to the unknot. We show…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
In last few years there are major changes and evolution has been done on classification of data. As the application area of technology is increases the size of data also increases. Classification of data becomes difficult because of…
Let n be an even positive integer and F be the field \GF(2). A word in F^n is called balanced if its Hamming weight is n/2. A subset C \subseteq F^n$ is called a balancing set if for every word y \in F^n there is a word x \in C such that y…
Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. In…
The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second…
Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…
There are many real-world classification problems wherein the issue of data imbalance (the case when a data set contains substantially more samples for one/many classes than the rest) is unavoidable. While under-sampling the problematic…
The notion of semi-BCI algebras is introduced and some of its properties are investigated. This algebra is another generalization for BCI-algebras. It arises from the "intervalization" of BCI algebras. Semi-BCI have a similar structure to…
A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…
We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality…
Let $(X,\mu,T_1,...,T_l)$ be a measure-preserving system with those $T_i$ are commuting. Suppose that the polynomials $p_1(t),...,p_{l}(t)\in\Z[t]$ with $p_j(0)=0$ have distinct degrees. Then for any $\epsilon>0$ and $A\subseteq X$ with…
We present examples of multiplicative semigroups of positive reals (Beurling's generalized integers) with gaps bounded from below.
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…
In this paper we show derivations among logarithmic space bounded counting classes based on closure properties of $\#L$ that leads us to the result that $NL=C_=L\subseteq PL$.
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
This addendum shows that a demographic grade gap is best understood using a course deficit model rather than the more common student deficit model. Students from a concepts-first class took the same final exam as the three other classes…