A p-Adic Matter in a Closed Universe

In this paper, we introduce a new type of matter that has origin in p-adic strings, i.e., strings with a p-adic worldsheet. We investigate some properties of this p-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for p-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe. At the end, we discuss the obtained results, i.e., computed mass of the scalar p-adic particle, estimated radius of related closed universe and noted p-adic matter as a possible candidate for dark matter.

A golden probe of nonlinear Higgs dynamics

The most salient generic feature of a composite Higgs boson resides in the nonlinearity of its dynamics, which arises from degenerate vacua associated with the pseudo-Nambu–Goldstone (PNGB) nature of the Higgs boson. It has been shown that the nonlinear Higgs dynamics is universal in the IR and controlled only by a single parameter f, the decay constant of the PNGB Higgs. In this work we perform a fit, for the first time, to Wilson coefficients of $${\mathcal {O}}(p^4)$$ O ( p 4 ) operators in the nonlinear Lagrangian using the golden H $$\rightarrow $$ → 4L decay channel. By utilizing both the “rate” information in the signal strength and the “shape” information in the fully differential spectra, we provide limits on the Goldstone decay constant f, as well as $${\mathcal {O}}(p^4)$$ O ( p 4 ) Wilson coefficients, using Run 2 data at the LHC. In rate measurements alone, the golden channel prefers a negative $$\xi =v^2/f^2$$ ξ = v 2 / f 2 corresponding to a non-compact coset structure. Including the shape information, we identify regions of parameter space where current LHC constraint on f is still weak, allowing for $$\xi \lesssim 0.5$$ ξ ≲ 0.5 or $$\xi \gtrsim -0.5$$ ξ ≳ - 0.5 . We also comment on future sensitivity at the high-luminosity upgrade of the LHC which could allow for simultaneous fits to multiple Wilson coefficients.

Symmetry and conservation laws for tuberculosis model

In this paper, three-dimensional system of the tuberculosis (TB) model is reduced into a two-dimensional first-order and one-dimensional second-order differential equations. We use the method of Jacobi last multiplier to construct linear Lagrangians of systems of two first-order ordinary differential equations and nonlinear Lagrangian of the corresponding single second-order equation. The Noether's theorem is used for determining conservation laws. We apply the techniques of symmetry analysis to a model to identify the combinations of parameters which lead to the possibility of the linearization of the system and provide the corresponding solutions.

The Rate of Convergence of a NLM Based on F–B NCP for Constrained Optimization Problems Without Strict Complementarity

It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer–Burmeister (F–B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second-order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians

Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous.

Convergence Theory of a SAA Method for Min-Max Stochastic Optimization Problems

Min-max stochastic optimization is a kind of important problems in stochastic optimization, which has been widely applied in subjects such as inventory theory and robust optimization and engineering field. In this paper, we present sample average approximation(SAA) method for a class of min-max stochastic optimization problems, based on a nonlinear Lagrangian function. Convergence of the SAA estimators are analyzed by means of epi-convergence theory,when the Lagrange multiplier vector is optimal and the parameter is small enough.