arXiv research

Improved method for numerical conformal mappings on complex domains.

This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain $S$ onto a punctured disk $D_S$ associated with a given Beltrami differential. The Beltrami differential, which me…

We establish existence and uniqueness of compact graphs of constant mean curvature in MxR over bounded multiply connected domains of Mx{0} with boundary lying in two parallel horizontal slices of MxR

The paper finds the largest eigenvalue for a specific type of domain in hyperbolic space.

The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.

We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and critical points of the Green's function. The principal idea used is an affine scaling…

Study dynamics of $L^p$-multipliers on harmonic manifolds with exponential volume growth.

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

Method flattens complex surfaces with consistent density and shape.

The restricted class of quasicircles sometimes called the "Weil-Petersson-class" has been a subject of interest in the last decade. In this paper we establish a Sokhotski-Plemelj jump formula for WP-class quasicircles, for boundary data in a certain conformally invariant Besov space. We show that this Besov space is pr…

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…

The paper extends affine connection results to singular warped and twisted products.

In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and 2-Killing vector fields on multiply warped products.

The study finds lower bounds for the first eigenvalue of the Laplacian in planar domains with magnetic fields.

Two novel algorithms for conformal parameterization of multiply-connected surfaces.

Upper bounds for magnetic Laplacian eigenvalues on planar domains.

Article establishes criteria for multiplier Hermitian-Einstein metrics on KSM-manifolds.

A new algorithm speeds up matrix multiplication without actual multiplication.

The aim of this work is to link the quasiconformal geometry of a Euclidean domain $U$ to the spectral properties of its Dirichlet integral $\D$, through the algebra of multipliers $\M(H^{1,2}(U))$ of the Sobolev space. In the main result we prove that a homeomorphism $γ:U\toγ(U)$ between Euclidean domains, giving rise …

Derives formula for present value of future consumer goods multiplier.

Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…

Classifies multiply-transitive (2,3,5)-distributions using modern Cartan geometry.

Extending Lévi-Civita's concept to non-quadratic spaces, this study finds extremal compatible linear connections.

Study proves rigidity of certain gradient steady Ricci solitons with harmonic Weyl curvature.

Developed an ellipsoidal density-equalizing map for genus-0 closed surfaces.

The paper resolves a problem about metric inequivalence and characterizes proper holomorphic maps.

The paper explores the correspondence between gradient flow lines of a function and its Lagrange multiplier functional.

Local norms of Fourier multipliers bounded on discrete subgroups of Lie groups.

Method estimates network connectivity and dimensionality from multiple networks.

Using the characterization of last multipliers as solutions of the Liouville's transport equation, new results are given in this approach of ODE by providing several new characterizations, e.g. in terms of Witten and Marsden differentials or adjoint vector field. Applications to Hamiltonian vector fields on Poisson man…

We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equati…

New unoriented versions of Schur and Bogomolov multipliers for finite groups.

This paper presents by simulation how approximate multipliers can be utilized to enhance the training performance of convolutional neural networks (CNNs). Approximate multipliers have significantly better performance in terms of speed, power, and area compared to exact multipliers. However, approximate multipliers have…

Method improves model performance on segments with local distribution shifts.

The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size $s$ when $s$ is larger than some crossover scale, providing direct evidence of the existence of sca…

Domain adaptation (DA) addresses the real-world image classification problem of discrepancy between training (source) and testing (target) data distributions. We propose an unsupervised DA method that considers the presence of only unlabelled data in the target domain. Our approach centers on finding matches between sa…

Study approximates operator learning for PDEs using Fourier multipliers.

Numerical methods solve Steklov eigenvalue problems to generate free boundary minimal surfaces.

New framework assesses LLMs' expertise using nonparametric ranking and confidence diagrams.

Paper tackles efficient risk estimation under dataset shift conditions.

Information in neural networks is represented as weighted connections, or synapses, between neurons. This poses a problem as the primary computational bottleneck for neural networks is the vector-matrix multiply when inputs are multiplied by the neural network weights. Conventional processing architectures are not well…

In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in nonc…

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

Historically, the banking multiplier has been in a range of 4 to 100, with 25% to 1% reserve ratios at most layers of the banking system encompassing the majority of its range in recent centuries. Here it is shown that multipliers over 1 000 can occur from a new mechanism in banking. This new multiplier uses a default …

We extend Nadel's results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author. Applying our extension we can determine the multiplier ideal sheaves on toric del Pezzo surfaces which do not admit Kähler-Einstein metrics. We also show t…

The study uses historical revenue data to forecast music catalog cashflows and multipliers.

We present an elementary analysis of the dynamical aspects of the GDP / government surplus multiplier with relevance to the assessment of a country's debt repayment policy. We show the (at first) counter intuitive result that in order to reduce the Debt/GDP ratio, countries with high Debt to GDP should go into further …