We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background are found.

P. Bozhilov

We consider null bosonic p-branes moving in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null string and the null membrane in Demianski-Newman background are found.

P. Bozhilov B. Dimitrov

We show that a $3-$dimensional paracontact manifold on which $Q\varphi =\varphi Q$ is either a manifold with $trh^2=0$, flat or of constant $\xi-$sectional curvature $k\neq-1$ and constant $\varphi$-sectional curvature $-k\neq 1$.

Simeon Zamkovoy Assen Bojilov

We prove that if a mapping F:X to Y, where X and Y are Banach spaces, is metrically regular at x for y and its inverse F^{-1} is convex and closed valued locally around (x,y), then for any function G:X to Y with lip G(x)regF(x|y)) < 1, the mapping (F+G)^{-1} has a continuous local selection around (x, y+G(x)) which is also calm.

Asen L. Dontchev

This paper strives to predict fine-grained fashion similarity. In this similarity paradigm, one should pay more attention to the similarity in terms of a specific design/attribute between fashion items. For example, whether the collar designs of the two clothes are similar. It has potential value in many fashion related applications, such as fashion copyright protection. To this end, we propose an Attribute-Specific Embedding Network (ASEN) to jointly learn multiple attribute-specific embeddings, thus measure the fine-grained similarity in the corresponding space. The proposed ASEN is comprised of a global branch and a local branch. The global branch takes the whole image as input to extract features from a global perspective, while the local branch takes as input the zoomed-in region-of-interest (RoI) w.r.t. the specified attribute thus able to extract more fine-grained features. As the global branch and the local branch extract the features from different perspectives, they are complementary to each other. Additionally, in each branch, two attention modules, i.e., Attribute-aware Spatial Attention and Attribute-aware Channel Attention, are integrated to make ASEN be able to locate the related regions and capture the essential patterns under the guidance of the specified attribute, thus make the learned attribute-specific embeddings better reflect the fine-grained similarity. Extensive experiments on three fashion-related datasets, i.e., FashionAI, DARN, and DeepFashion, show the effectiveness of ASEN for fine-grained fashion similarity prediction and its potential for fashion reranking. Code and data are available at https://github.com/maryeon/asenpp .

Jianfeng Dong Zhe Ma Xiaofeng Mao Xun Yang Yuan He Richang Hong Shouling Ji

We theoretically propose and experimentally demonstrate a novel composite polarization controller. With our design, which comprises two half-wave plates and two quarter-wave plates the retardance and rotation can be changed continuously by simply rotating the half-wave plates. The idea is universal since any commercial half and quarter-wave plates may be used to achieve any desired polarization change.

Hristina Hristova Hristo Iliev Ivayla Bozhinova Andon Rangelov Asen Pashov

We consider a model for tensionless (null) super p-branes with N chiral supersymmetries in ten dimensional flat space-time. After establishing the symmetries of the action, we give the general solution of the classical equations of motion in a particular gauge. In the case of a null superstring (p=1) we find the general solution in an arbitrary gauge. Then, using a harmonic superspace approach, the initial algebra of first and second class constraints is converted into an algebra of Lorentz-covariant, BFV-irreducible, first class constraints only. The corresponding BRST charge is as for a first rank dynamical system.

P. Bozhilov

We consider null bosonic p-branes moving in curved space-times and develop a method for solving their equations of motion and constraints, which is suitable for string theory backgrounds. As an application, we give an exact solution for such background in ten dimensions.

P. Bozhilov

We show how the classical string dynamics in $D$-dimensional curved background can be reduced to the dynamics of a massless particle constrained on a certain surface whenever there exists at least one Killing vector for the background metric. Then we obtain a number of sufficient conditions, which ensure the existence of exact solutions to the equations of motion and constraints. The results are also relevant to the null string case. Finally, we illustrate our considerations with an explicit example in four dimensions.

P. Bozhilov

We consider the classical null p-brane dynamics in D-dimensional curved backgrounds and apply the Batalin-Fradkin-Vilkovisky approach for BRST quantization of general gauge theories. Then we develop a method for solving the tensionless $p$-brane equations of motion and constraints. This is possible whenever there exists at least one Killing vector for the background metric. It is shown that the same method can be also applied for the tensile 1-branes. Finally, we give two examples of explicit exact solutions in four dimensions.

P. Bozhilov