Bosonic η-deformed AdS4 × $$ \mathbbm{CP} $$3 background

We build the bosonic η-deformed AdS4 × $$ \mathbbm{CP} $$ CP 3 background generated by an r-matrix that satisfies the modified classical Yang-Baxter equation. In a special limit we find that it is the gravity dual of the noncommutative ABJM theory.

LREE of an unstable dressed-dynamical Dp-brane: superstring calculations

We obtain the left-right entanglement entropy (LREE) for a Dp-brane with tangential motion in the presence of a U(1) gauge potential, the Kalb–Ramond field and an open string tachyon field. Thus, at first we extract the Rényi entropy and then by taking a special limit of it we acquire the entanglement entropy. We shall investigate the behavior of the LREE under the tachyon condensation phenomenon. We observe that the deformation of the LREE, through this process, reveals the collapse of the brane. Besides, we examine the second law of thermodynamics for the LREE under tachyon condensation, and we extract the imposed constraints. Note that our calculations will be in the context of the type IIA/IIB superstring theories.

Pentagon integrals to arbitrary order in the dimensional regulator

We analytically calculate one-loop five-point Master Integrals, pentagon integrals, with up to one off-shell leg to arbitrary order in the dimensional regulator in d = 4−2𝜖 space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the Mathematica package HypExp. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.

Special Limit Condition Of Reinforced Concrete Structures And Its Normalization

One of the ways to improve the resilience of buildings in the event of failure of the bearing structure or emergency, seismic effects is a more complete account of the behavior of elements and their mates at short-term action of loads and dynamics of change of the scheme of the bearing system of the building. To do this, it is advisable to allow more cracks to open, the development of deflections and partial destruction of some sections, which contradicts the current criteria for the first and second limit states that ensure the operational suitability of structures and buildings. Therefore, it is necessary to introduce specific standards of a special limit state for structures. A special limit state is the stage of operation of the structure after reaching the load-bearing capacity for the first and the deformation limits for the second limit states. Exceeding this state, in which the structures do not fully meet the functional requirements, leads to their collapse. The implementation of this limit state is most appropriate in load-bearing systems with a high degree of static indeterminability and constructive interaction of all bearing elements. The introduction and consideration of a special limit stress-strain state of reinforced concrete structures make it possible to detect significant strength and deformation reserves, even after significant fragmentation of the compressed concrete zone and, as a result, reducing the working section of the structure. As the main criteria of a particular limit state for reinforced concrete structures, it is recommended to adopt: the ultimate deformations of compressed concrete and tensile reinforcement with higher values than permissible under normal conditions; as well as the deflections of elements, provided that the minimum allowable length of the zone of bearing and anchorage of reinforcement.

String theory on AdS3 × M7 in the tensionless limit

We review old and recent results on a special limit of string theory on [Formula: see text] with pure NS–NS fluxes: the limit in which the string length [Formula: see text] equals the [Formula: see text] radius [Formula: see text]. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the noncompactness of the boundary CFT target space, and on how these features change when the point [Formula: see text] is approached. Also, we briefly review the recent proposals for exact realizations of AdS/CFT correspondence at this special point.

Centered Polygonal Lacunary Sequences

Lacunary functions based on centered polygonal numbers have interesting features which are distinct from general lacunary functions. These features include rotational symmetry of the modulus of the functions and a notion of polished level sets. The behavior and characteristics of the natural boundary for centered polygonal lacunary sequences are discussed. These systems are complicated but, nonetheless, well organized because of their inherent rotational symmetry. This is particularly apparent at the so-called symmetry angles at which the values of the sequence at the natural boundary follow a relatively simple 4 p -cycle. This work examines special limit sequences at the natural boundary of centered polygonal lacunary sequences. These sequences arise by considering the sequence of values along integer fractions of the symmetry angle for centered polygonal lacunary functions. These sequences are referred to here as p-sequences. Several properties of the p-sequences are explored to give insight in the centered polygonal lacunary functions. Fibered spaces can organize these cycles into equivalence classes. This then provides a natural way to approach the infinite sum of the actual lacunary function. It is also seen that the inherent organization of the centered polygonal lacunary sequences gives rise to fractal-like self-similarity scaling features. These features scale in simple ways.

Covariant perturbations in the gonihedric string model

We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends on the square root of the quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, [Formula: see text], living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for [Formula: see text].