Related papers: On some new hook-content identities
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.
We prove two partition identities which are dual to the Rogers-Ramanujan identities. These identities are inspired by (and proved using) a correspondence between three kinds of objects: a new type of partitions (neighborly partitions),…
In this paper we give new identities involving q-Euler polynomials of higher order.
Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable…
The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum…
Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of…
If I know of a few persons of interest, how can a combination of human language technology and graph theory help me find other people similarly interesting? If I know of a few people committing a crime, how can I determine their…
The Covid-19 pandemic has made individuals and organizations to rethink the way of handling identity verification and credentials sharing particularly in quarantined situations. In this study, we investigate the inefficiencies of…
Many assumptions that underpin human concepts of identity do not hold for machine minds that can be copied, edited, or simulated. We argue that there exist many different coherent identity boundaries (e.g.\ instance, model, persona), and…
Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing. In this Letter, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed [Phys. Rev. Lett.…
The task of providing effective instruction and facilitating comprehension of resources is a substantial difficulty in the field of Quantum Computing, mostly attributable to the complicated nature of the subject matter. Our research-based…
In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers…
Identity-based software signing tools aim to make software artifact provenance verifiable while reducing the operational burden of long-lived key management. However, there is limited cross-tool longitudinal evidence about which usability…
Cross-modal retrieval aims to search for data with similar semantic meanings across different content modalities. However, cross-modal retrieval requires huge amounts of storage and retrieval time since it needs to process data in multiple…
The knowledge graph(KG) composed of entities with their descriptions and attributes, and relationship between entities, is finding more and more application scenarios in various natural language processing tasks. In a typical knowledge…
The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the…
To overcome the barrier of storage and computation, the hashing technique has been widely used for nearest neighbor search in multimedia retrieval applications recently. Particularly, cross-modal retrieval that searches across different…
Identity verification based on authenticity assessment of a handwritten signature is an important issue in biometrics. There are many effective methods for signature verification taking into account dynamics of a signing process. Methods…
In this paper we derive new identities satisfied by Chebyshev polynomials of the first kind and big q-Jacobi polynomials. An immediate benefit of the derived identities is the achievement of closed-form expressions for the Laurent…