Projective Tensor Research Articles

Characterizations for pseudoparalel submanifolds of Lorentz-Sasakian space forms

In this article, total geodesic submanifolds for Lorentz-Sasakian space forms are investigated. For these submanifolds, pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel invariant submanifolds have been studied and many new results have been obtained. In addition, necessary and sufficient conditions have been obtained for these submanifolds to be total geodesic on the concircular and projective curvature tensors.

Modeling the cell-type-specific mesoscale murine connectome with anterograde tracing experiments.

The Allen Mouse Brain Connectivity Atlas consists of anterograde tracing experiments targeting diverse structures and classes of projecting neurons. Beyond regional anterograde tracing done in C57BL/6 wild-type mice, a large fraction of experiments are performed using transgenic Cre-lines. This allows access to cell-class-specific whole-brain connectivity information, with class defined by the transgenic lines. However, even though the number of experiments is large, it does not come close to covering all existing cell classes in every area where they exist. Here, we study how much we can fill in these gaps and estimate the cell-class-specific connectivity function given the simplifying assumptions that nearby voxels have smoothly varying projections, but that these projection tensors can change sharply depending on the region and class of the projecting cells. This paper describes the conversion of Cre-line tracer experiments into class-specific connectivity matrices representing the connection strengths between source and target structures. We introduce and validate a novel statistical model for creation of connectivity matrices. We extend the Nadaraya-Watson kernel learning method that we previously used to fill in spatial gaps to also fill in gaps in cell-class connectivity information. To do this, we construct a "cell-class space" based on class-specific averaged regionalized projections and combine smoothing in 3D space as well as in this abstract space to share information between similar neuron classes. Using this method, we construct a set of connectivity matrices using multiple levels of resolution at which discontinuities in connectivity are assumed. We show that the connectivities obtained from this model display expected cell-type- and structure-specific connectivities. We also show that the wild-type connectivity matrix can be factored using a sparse set of factors, and analyze the informativeness of this latent variable model.

Seismotectonic Stress Regime and Airborne-Gravity Lineament Investigation of the Caribbean region and its Kinematic implications

The tectonic stress regime of the Caribbean region has been studied by stress tensor inversion analysis for the area bounded by Latitudes 17.32o to 23.79o N and Longitudes 81.47o to -60.56o E. A total of two hundred and twenty (220) fault plane solutions (FPS), made up of the seismic (earthquake) events that have occurred in the region of the study were found on the data catalog of the project website of the global centroid moment tensor, were employed in this study. To characterize the stress regimes of the region of study, the classification of the region based on the global moment tensor project is as follows: Cuba-zone, Haiti-zone, Dominican-republic, Monapassage, Puerto Rico, Virgin-Island and the Leeward Island. The gravity geophysical method revealed the presence of multiple or swarms of fractured lines within the same geographical range of study which might have developed over the years as a result of the interaction and coupling effect of the plate boundaries that have close proximity to the region of study. The seismicity pattern indicates that none of the provinces or countries located within the Caribbean region is devoid of large-magnitude earthquake occurrences capable of wreaking severe havoc on the immediate environment. Obviously, our stress tensor inversion result indicates two types of stress regimes namely compression and the strike-slip with different orientations. Cuba-zone, Haiti-zone, Dominican Republic, Monapassage, and Leeward Island are governed mainly by compression stress regimes. In contrast, the strike-slip stress regimes mainly govern the Puerto Rico and the Virgin Island.

Some properties of 𝑝-limited sets

Karn and Sinha [Glasg. Math. J. 56 (2014), pp. 427–437] introduced the p p -limited ( 1 ≤ p > ∞ 1 \leq p > \infty ) sets (see the definition below). We show that p p -limited sets are preserved by continuous polynomials as well as by the projective tensor product and that scalar-valued polynomials are p p -summable on p p -limited sets. Considering the notion of p p -limited set from the ℓ p \ell _p -valued operators point of view, we introduce in Section \ref{sec:3} two weaker types of p p -limitedness in the setting of Banach lattices and study their basic properties.

Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold

The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in an LP-Sasakian manifold to its tangent bundle are investigated. Necessary and sufficient conditions for the lifts of the Ricci tensor to be symmetric and skew-symmetric and the lifts of the projective Ricci tensor to be skew-symmetric in the tangent bundle are given. An example of complete lifts of four-dimensional LP-Sasakian manifolds in the tangent bundle is shown.

Projective freeness and Hermiteness of complex function algebras

The paper studies projective freeness and Hermiteness of algebras of complex-valued continuous functions on topological spaces, Stein algebras, and commutative unital Banach algebras. New sufficient cohomology conditions on the maximal ideal spaces of the algebras are given that guarantee the fulfilment of these properties. The results are illustrated by nontrivial examples. Based on the Borsuk theory of shapes, a new class C of commutative unital complex Banach algebras is introduced (an analog of the class of local rings in commutative algebra) such that the projective tensor product with algebras in C preserves projective freeness and Hermiteness. Some examples of algebras of class C and of other projective free and Hermite function algebras are assembled. These include, e.g., Douglas algebras, finitely generated algebras of symmetric functions, Bohr-Wiener algebras, algebras of holomorphic semi-almost periodic functions, and algebras of bounded holomorphic functions on Riemann surfaces.

On Generalized Recurrent Finsler Spaces of Higher Order with Berwald’s Curvature Tensor

In this present paper, we introduced a Finsler space Fn which projective curvature tensor K^i_ijkh satisfies the generalized five recurrence property with respect to Berwald’s connection parameters G^i_kh, we have derived some theorems and some identities along with few more related results in a recurrent and generalized 5-recurrent Finsler space with Berwald’s curvature tensor field.

Weak precompactness in projective tensor products

We give a sufficient condition for a pair of Banach spaces (X,Y) to have the following property: whenever W1⊆X and W2⊆Y are sets such that {x⊗y:x∈W1,y∈W2} is weakly precompact in the projective tensor product X⊗̂πY, then either W1 or W2 is relatively norm compact. For instance, such a property holds for the pair (ℓp,ℓq) if 1<p,q<∞ satisfy 1/p+1/q≥1. Other examples are given that allow us to provide alternative proofs to some results on multiplication operators due to Saksman and Tylli. We also revisit, with more direct proofs, some known results about the embeddability of ℓ1 into X⊗̂πY for arbitrary Banach spaces X and Y, in connection with the compactness of all operators from X to Y∗.

Extremal Structure of Projective Tensor Products

We prove that, given two Banach spaces X and Y and bounded, closed convex sets Csubseteq X and Dsubseteq Y, if a nonzero element zin {overline{{{,textrm{co},}}}}(Cotimes D)subseteq Xwidehat{otimes }_pi Y is a preserved extreme point then z=x_0otimes y_0 for some preserved extreme points x_0in C and y_0in D, whenever K(X,Y^*) separates points of X widehat{otimes }_pi Y (in particular, whenever X or Y has the compact approximation property). Moreover, we prove that if x_0in C and y_0in D are weak-strongly exposed points then x_0otimes y_0 is weak-strongly exposed in {overline{{{,textrm{co},}}}}(Cotimes D) whenever x_0otimes y_0 has a neighbourhood system for the weak topology defined by compact operators. Furthermore, we find a Banach space X isomorphic to ell _2 with a weak-strongly exposed point x_0in B_X such that x_0otimes x_0 is not a weak-strongly exposed point of the unit ball of Xwidehat{otimes }_pi X.

Study of a Projective Ricci Semi-symmetric Nearly Kaehler Manifold

We inaugurate a new curvature properties of projective curvature tensor in nearly Kaehler manifold. We defined projective Ricci semi-symmetric quasi-Einstein nearly Kaehler manifold, Projective Ricci semisymmetric generalised quasi-Einstein nearly Kaehler manifold and a Projective Ricci semi-symmetric pseudo generalised quasi-Einstein nearly Kaehler manifold and also found some results in the manifold.

Concircularly semi-symmetric metric connection

Results on a concircularly semi-symmetric metric connection on a Riemannian manifold are presented. Six linearly independent curvature tensors with respect to this non-symmetric linear connection are studied, and the tensors coincident with the Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are determined. Transformations of connections when the Riemannian curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are invariant are also observed. Moreover, new conditions for the Einstein manifold are derived.

Several Remarks on Norm Attainment in Tensor Product Spaces

The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if Xwidehat{otimes }_pi Y is strongly subdifferentiable and either X or Y has the metric approximation property then every bounded operator from X to Y^* is compact. We also prove that (ell _p(I)widehat{otimes }_pi ell _q(J))^* has the w^*-Kadec-Klee property for every non-empty sets I, J and every 2<p,q<infty , obtaining in particular that the norm of the space ell _p(I)widehat{otimes }_pi ell _q(J) is strongly subdifferentiable. This extends several results of Dantas, Kim, Lee and Mazzitelli. We also find examples of spaces X and Y for which the set of norm-attaining tensors in Xwidehat{otimes }_pi Y is dense but whose complement is dense too.

Quarter-Symmetric Metric Connection on a Cosymplectic Manifold

We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define η-Einstein cosymplectic manifolds of the θ-th kind and prove that they coincide with the η-Einstein cosymplectic manifold.

On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection

In the present paper, we have studied the curvature properties of the Schouten-van Kampen connection on the n-dimensional Para Sasakian manifold and obtained some new results. Also, we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the Para-Sasakian manifold with respect to the Schouten-van Kampen connection.

On Hyperbolic HSU -Structure Manifold,Recurrent and Symmetry

In this paper, we have defined recurrence and symmetry of different kinds in Hsu-structure manifold. Some theorem establishing relationship between different kinds of recurrent H- HSU-Structure manifold involving equivalent conditions with respect to projective, conformal, conharmonic and concircular curvature tensors has been discussed recurrence parameter have also been studied.

Some isomorphic properties in projective tensor products

Some isomorphic properties in projective tensor products

Class Nearly kahler Manifold of W – Projective Curvature Tensor

The current study deals with new three classes of the manifold of w – projective curvature tensor. The aim of this paper to calculate differential - geometrical and topological properties closest for new classes , and , through it ,an equivalence relationship was obtained between these classes and one of or more the tensor compounds and the components of curvature tensor and with adjoint G-structure space. Finally, we discover a relationship between , , with each other.

Three-loop helicity amplitudes for photon+jet production

We present three-loop helicity amplitudes for the production of a single photon in association with one jet in Quantum Chromodynamics, a final state which provides a standard candle of the Standard Model at the Large Hadron Collider. We employ a recently-proposed variation of the so-called tensor projection method in the 't Hooft-Veltman scheme (tHV) which avoids the computation of contributions due to unphysical (-2$\epsilon$)-dimensional polarisations of the external states. We obtain compact analytic results expressed in terms of harmonic polylogarithms.

Some geometric and physical properties of pseudo m*-projective symmetric manifolds

In this study we introduce a new tensor in a semi-Riemannian manifold, named the M*-projective curvature tensor which generalizes the m-projective curvature tensor. We start by deducing some fundamental geometric properties of the M*-projective curvature tensor. After that, we study pseudo M*-projective symmetric manifolds (PM?S)n. A non-trivial example has been used to show the existence of such a manifold. We introduce a series of interesting conclusions. We establish, among other things, that if the scalar curvature ? is non-zero, the associated 1-form is closed for a (PM?S)n with divM* = 0. We also deal with pseudo M*-projective symmetric spacetimes, M*-projectively flat perfect fluid spacetimes, and M*-projectively flat viscous fluid spacetimes. As a result, we establish some significant theorems.

On generalized projective curvature tensor of para-Kenmotsu manifolds

On generalized projective curvature tensor of para-Kenmotsu manifolds