Related papers: Generalized upper and lower Legendre conjugates fo…
Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
The Legendre transform (LET) is a product of a general duality principle: any smooth curve is, on the one hand, a locus of pairs, which satisfy the given equation and, on the other hand, an envelope of a family of its tangent lines. An…
Complex Legendre duality is a generalization of Legendre transformation from Euclidean spaces to Kahler manifolds, that Berndtsson and collaborators have recently constructed. It is a local isometry of the space of Kahler potentials. We…
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…
We consider a basis of square integrable functions on a rectangle, contained in $R^2$, constructed with Legendre polynomials, suitable, for instance, for the analogical description of images on the plane or in other fields of application of…
We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at…
Model merging aims to build a multi-task learner by combining the parameters of individually fine-tuned models without additional training. While a straightforward approach is to average model parameters across tasks, this often results in…
Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…
A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates $u(z)= o(y^{1-\alpha}|z|^{m+\alpha})$ at infinity in the upper half plane ${\bf C}_{+}$, which generalizes the growth properties of…
In this paper, usual Sturm-Liouville problems are extended for symmetric functions so that the corresponding solutions preserve the orthogonality property. Two basic examples, which are special cases of a generalized Sturm-Liouville…
A relationship between partial derivatives of the associated Legendre function of the first kind with respect to its degree, $[\partial P_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$, and to its order, $[\partial P_{n}^{\mu}(z)/\partial\mu]_{\mu=m}$,…
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it…
In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in $D$ dimensional…
Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space $\Phi^\times$ in a convenient Gelfand triplet…
We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p-L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for…