$$\alpha $$-attractors from supersymmetry breaking

We construct new models of inflation and spontaneous supersymmetry breaking in de Sitter vacuum, with a single chiral superfield, where inflaton is the superpartner of the goldstino. Our approach is based on hyperbolic Kähler geometry, and a gauged (non-axionic) $$U(1)_R$$ U ( 1 ) R symmetry rotating the chiral scalar field by a phase. The $$U(1)_R$$ U ( 1 ) R gauge field combines with the angular component of the chiral scalar to form a massive vector, and single-field inflation is driven by the radial part of the scalar. We find that in a certain parameter range they can be approximated by simplest Starobinsky-like (E-model) $$\alpha $$ α -attractors, thus predicting $$n_s$$ n s and r within $$1\sigma $$ 1 σ CMB constraints. Supersymmetry (and R-symmetry) is broken at a high scale with the gravitino mass $$m_{3/2} > rsim 10^{14}$$ m 3 / 2 ≳ 10 14 GeV, and the fermionic sector also includes a heavy spin-1/2 field. In all the considered cases the inflaton is the lightest field of the model.

COMBUSTION OF A GAS SUSPENSION OF COAL DUST IN A SWIRLING FLOW

Swirling combustion is currently one of the most important engineering problems in physics of combustion. There is a hypothesis on the increase in the combustion efficiency of reacting gas mixtures in combustion chambers with swirling flows, as well as on the increase in the efficiency of fuel combustion devices. In this paper, it is proposed to simulate a swirling flow by taking into account the angular component of the flow velocity. The aim of the study is to determine the effect of the angular component of the flow velocity on the characteristics of the flow and combustion of an air suspension of coal dust in a pipe. The problem is solved in a twodimensional axisymmetric approximation with allowance for a swirling flow. A physical and mathematical model is based on the approaches of the mechanics of multiphase reacting media. A solution method involves the arbitrary discontinuity decay algorithm. The impact of the flow swirl and the size of coal dust particles on the gas temperature distribution along the pipe is determined.

On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations

We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of $$\Vert {v_{r}}/{\sqrt{r^3}}\Vert _{L_2({\mathbb {R}}^3\times (0,T))}$$‖vr/r3‖L2(R3×(0,T)) as well as boundedness of $$\Vert {\omega _{\varphi }}/{\sqrt{r}} \Vert _{L_2({\mathbb {R}}^3\times (0,T))}$$‖ωφ/r‖L2(R3×(0,T)), where $$v_r$$vr is the radial component of velocity and $$\omega _{\varphi }$$ωφ is the angular component of vorticity, imply regularity of weak solutions.

Differential-Henselian Fields with Many Constants

This chapter considers differential-henselian fields with many constants. Here d-henselian includes having small derivation, so d-henselian valued differential fields with many constants are monotone. The goal here is to derive Scanlon's extension in [382, 383] of the Ax-Kochen-Eršov theorems to d-henselian valued differential fields with many constants. Among the results to be established is Theorem 8.0.1: Suppose K and L are d-henselian valued differential fields with many constants. Then K = L as valued differential fields if and only if res K = res L as differential fields and Γ‎ subscript K = Γ‎ subscript L as ordered abelian groups. The chapter also discusses an angular component map on K, equivalence over substructures, relative quantifier elimination, and a model companion.

Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions

By considering the extreme behavior of bivariate random vectors with a polar representation R(u(T), v(T)), it is commonly assumed that the radial component R and the angular component T are stochastically independent. We investigate how to relax this rigid independence assumption such that conditional limit theorems can still be deduced. For this purpose, we introduce a novel measure for the dependence structure and present convenient criteria for validity of limit theorems possessing a geometrical meaning. Thus, our results verify a stability of the available limit results, which is essential in applications where the independence of the polar components is not necessarily present or exactly fulfilled.

0-D-valued fields

In [12]. T. Scanlon proved a quantifier elimination result for valued D-fields in a three-sorted language by using angular component functions. Here we prove an analogous theorem in a different language which was introduced by F. Delon in her thesis. This language allows us to lift the quantifier elimination result to a one-sorted language by a process described in the Appendix. As a byproduct, we state and prove a “positivstellensatz” theorem for the differential analogue of the theory of real-series closed fields in the valued D-field setting.

ON THE QUINTESSENCE WITH ABELIAN AND NON-ABELIAN SYMMETRY

We study the perturbations on both "radial" and "angular" components of the quintessence with an internal Abelian and non-Abelian symmetry. The properties of the perturbation on the "radial" component depend on the specific potential of the model and is similiar for both Abelian and non-Abelian case. We show that the cosine-type potential is very interesting for the O (N) quintessence model and also give a critical condition of instability for the potential. While the properties of perturbations on "angular" components depend on whether the internal symmetry is Abelian or non-Abelian, which we have discussed respectively. In the non-Abelian case, the fluctuation of the "angular" component will increase rapidly with time while in the Abelian case it will not.

ANGULAR INFLATION FROM SUPERGRAVITY

We study supergravity inflationary models where inflation is produced along the angular direction. For this we express the scalar component of a chiral superfield in terms of the radial and the angular components. We then express the supergravity potential in a form particularly simple for calculations involving polynomial expressions for the superpotential and Kähler potential. We show for a simple Polonyi model the angular direction may give rise to a stage of inflation when the radial field is fixed to its minimum. We obtain analytical expressions for all the relevant inflationary quantities and discuss the possibility of supersymmetry breaking in the radial direction while inflating by the angular component.

On the angular component map modulo P

In [10] we introduced a new first order language for valued fields. This language has three sorts of variables, namely variables for elements of the valued field, variables for elements of the residue field and variables for elements of the value group. contains symbols for the standard field, residue field, and value group operations and a function symbol for the valuation. Essential in our language is a function symbol for an angular component map modulo P, which is a map from the field to the residue field (see Definition 1.2).For this language we proved a quantifier elimination theorem for Henselian valued fields of equicharacteristic zero which possess such an angular component map modulo P [10, Theorem 4.1]. In the first section of this paper we give some partial results on the existence of an angular component map modulo P on an arbitrary valued field.By applying the above quantifier elimination theorem to ultraproducts ΠQp/D, we obtained a quantifier elimination, in the language , for the p-adic field Qp; and this elimination is uniform for almost all primes p [10, Corollary 4.3]. In §2 we prove that our language is essentially stronger than the natural language for p-adic fields in the sense that the angular component map modulo P cannot be defined, uniformly for almost all p, in terms of the natural language for p-adic fields.