In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional
For each quadratic form Q in Quad(V) over a given vector space over a field R we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form $x x-Q(x),x...
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <-> \bigwedg...
JavaScript is a popular attack vector for releasing malicious payloads on unsuspecting Internet users. Authors of this malicious JavaScript often employ numerous obfuscation techniques in order to prevent the automatic detection by antivirus and hind...
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars
Many epidemiological and clinical studies use accelerometry to objectively measure physical activity using the activity counts, vector magnitude, or number of steps. These measures use just a fraction of the information in the raw accelerometry data...
I construct a global version of the local polysymplectic approach to covariant Hamiltonian field theory pioneered by C. Gunther. Beginning with the geometric framework of the theory, I specialize to vertical vector fields to construct the (poly)sympl...
Recently we have obtained the Cartan connection for the Finsler space whose metric is given by an exponential change with an h-vector. In this paper, we discuss certain geometric properties of a Finslerian hyperspace subjected to an h-exponential cha...
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the ordinary geo...
We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce and study weak versions of the absc...
We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. Using initial monomials, projections of the underlying vect...
Vector field library using discrete exterior culclus (⭐ 77)
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
We present results at beta=6.0 and 6.2 for the O(a) improvement and renormalization constants for bilinear operators using axial and vector Ward identities. We discuss the extraction of the mass dependence of the renormalization constants and the c...
We study QCD in 2 dimensions using the improved lattice fermionic Hamiltonian proposed by Luo, Chen, Xu and Jiang. The vector mass and the chiral condensate are computed for various $SU(N_C)$ gauge groups. We do observe considerable improvement in...
The PHP Agentic Framework to build production-ready AI driven applications. Connect components (LLMs, vector DBs, memory) to agents that can interact with your data. With its modular architecture it's best suited for building RAG, multi-agent workflows, or bus…
Sub-image search with high accuracy in natural images still remains a challenging problem. This paper proposes a new feature vector called profile for a keypoint in a bag of visual words model of an image. The profile of a keypoint captures the spati...
This technical report describes the SJTU X-LANCE Lab system for the three tracks in CNSRC 2022. In this challenge, we explored the speaker embedding modeling ability of deep ResNet (Deeper r-vector). All the systems are only trained on the Cnceleb tr...
Enhanced LanceDB memory plugin for OpenClaw — Hybrid Retrieval (Vector + BM25), Cross-Encoder Rerank, Multi-Scope Isolation, Management CLI (⭐ 1508)
Open Lakehouse Format for Multimodal AI. Convert from Parquet in 2 lines of code for 100x faster random access, vector index, and data versioning. Compatible with Pandas, DuckDB, Polars, Pyarrow, and PyTorch with more integrations coming.. (⭐ 6147)