A Covariant Cauchy-Schwartz Measure’s Bounding Conditions to BSM Searches

Solving for the missing masses in the Higgs resonances, it was necessary to extend, even quantitatively via an index measurable amount, the SM using a threshold related longitudinal violation procedure. The obtained expression, by being non-contributing via its non-anomalously resulting parameter, is linked to a Cauchy-Schwartz 4-scalar product ratio type of two virtual Gauge Bosons momenta in its minimal anomalous configuration, as vs. its non-anomalous internal. Changing the bounds from energy into momenta, a convexity condition appears. Such technique clarifies the perturbative e.m. fields’ extensions into perturbative and non-perturbative QCD.In applications, there is the violation of the chiral insertion by the axion into neutrinos, and the Lepton number when passing form velocity to spin resonances, such confirming the CS procedure as plus the defiance of the SM comes through their branching ratios but not their angular distributions. Further which if remaining at the same level of minimization can restore the universality of extendibility in the Higgs self-couplings.Leading into deriving the phase of K0 → π+π-, in A(∆1=2)/A(∆1=0) so a conformal skipping dynamical shift from direct CP violation of D0 → K+K- and D0 → π+π- asymmetries, in the long-short mixing concords the phase of KL → π0ννbar, solving the KOTO anomaly.

ModMax meets Susy

We give a prescription for $$ \mathcal{N} $$ N = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.

Free transport for convex potentials

We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport maps between free Gibbs states associated to potentials which are far from quadratic, i.e., states which are far from the semicircle law. An essential technical ingredient in our approach is the extension of free stochastic analysis to non-commutative spaces of functions based on the Haagerup tensor product.

On the convexity condition for the Semi-Geostrophic system

We show that conservative distributional solutions to the Semi-Geostrophic systems in a rigid domain are in some well-defined sense critical points of a time-shifted energy functional involving measure-preserving rearrangements of the absolute density and momentum, which arise as one-parameter flow maps of continuously differentiable, compactly supported divergence free vector fields. We also show directly, with no recourse to Monge- Kantorovich theory, that the convexity requirement on the modified pressure potentials arises naturally if these critical points are local minimizers of said energy functional for any admis- sible vector field. The obligatory connection with the Monge-Kantorovich theory is addressed briefly.

Constrained preference elicitation

A planner wants to elicit information about an agent's preference relation, but not the entire ordering. Specifically, preferences are grouped into “types,” and the planner wants only to elicit the agent's type. We first assume that beliefs about randomization are subjective, and show that a space of types is elicitable if and only if each type is defined by what the agent would choose from some list of menus. If beliefs are objective, then additional type spaces can be elicited, though a convexity condition must be satisfied. These results remain unchanged when we consider a setting with multiple agents.

Modifying the convexity condition in Data Envelopment Analysis (DEA)

Conventional Data Envelopment Analysis (DEA) models are based on a production possibility set (PPS) that satisfies various postulates. Extension or modification of these axioms leads to different DEA models. In this paper, our focus concentrates on the convexity axiom, leaving the other axioms unmodified. Modifying or extending the convexity condition can lead to a different PPS. This adaptation is followed by a two-step procedure to evaluate the efficiency of a unit based on the resulting PPS. The proposed frontier is located between two standard, well-known DEA frontiers. The model presented can differentiate between units more finely than the standard variable return to scale (VRS) model. In order to illustrate the strengths of the proposed model, a real data set describing Iranian banks was employed. The results show that this alternative model outperforms the standard VRS model and increases the discrimination power of (VRS) models.

Existence of optimal controls for systems of controlled forward-backward doubly SDEs

We wish to study a class of optimal controls for problems governed by forward-backward doubly stochastic differential equations (FBDSDEs). Firstly, we prove existence of optimal relaxed controls, which are measure-valued processes for nonlinear FBDSDEs, by using some tightness properties and weak convergence techniques on the space of Skorokhod {\mathbb{D}} equipped with the S-topology of Jakubowski. Moreover, when the Roxin-type convexity condition is fulfilled, we prove that the optimal relaxed control is in fact strict. Secondly, we prove the existence of a strong optimal controls for a linear forward-backward doubly SDEs. Furthermore, we establish necessary as well as sufficient optimality conditions for a control problem of this kind of systems. This is the first theorem of existence of optimal controls that covers the forward-backward doubly systems.

CONVEXITY CONDITION OF THE GENERALIZED BERNATSKY INTEGRAL FOR ONE SUBCLASS OF STAR-LIKE FUNCTIONS

The article carried out a study on the convexity of the Bernatsky integral in the proposition that the function in question belongs to a subclass of star-shaped functions that satisfy certain conditions. For this, the condition of convexity of univalent functions was considered. The geometrical interpretation of the conditions is given, the radius of the convexity of the star-shaped functions is established. The intervals for the parameter are found for which the Bernatsky integral is a convex function in the whole unit circle, in cases where the parameter does not belong to the given interval, the Bernatsky integral will be a convex function in a circle of smaller radius. Three consequences are given in which various cases of convexity of the Bernatsky integral for analytic functions that belong to classes of functions with certain conditions are analyzed. For the considered classes of analytic functions, the radius of convexity of the Bernatsky integral is determined.

DISTINCT SOLUTIONS TO GENERATED JACOBIAN EQUATIONS CANNOT INTERSECT

We prove that if two $C^{1,1}(\unicode[STIX]{x1D6FA})$ solutions of the second boundary value problem for the generated Jacobian equation intersect in $\unicode[STIX]{x1D6FA}$ then they are the same solution. In addition, we extend this result to $C^{2}(\overline{\unicode[STIX]{x1D6FA}})$ solutions intersecting on the boundary, via an additional convexity condition on the target domain.