Admissible Space Research Articles

Dual topology of the Heisenberg motion groups

Let ℍn be the (2n + 1)-dimensional Heisenberg group, and let Tn be the n-dimensional torus acting on ℍn by automorphisms. In this paper, we describe the space of admissible coadjoint orbits of the Heisenberg motion group Gn = Tn ⋉ ℍn and we determine the topology of this space. We show that the bijection between the unitary dual Ĝn of Gn and its admissible coadjoint orbit space is a homeomorphism.

The global relaxation redistribution method for reduction of combustion kinetics.

An algorithm based on the Relaxation Redistribution Method (RRM) is proposed for constructing the Slow Invariant Manifold (SIM) of a chosen dimension to cover a large fraction of the admissible composition space that includes the equilibrium and initial states. The manifold boundaries are determined with the help of the Rate Controlled Constrained Equilibrium method, which also provides the initial guess for the SIM. The latter is iteratively refined until convergence and the converged manifold is tabulated. A criterion based on the departure from invariance is proposed to find the region over which the reduced description is valid. The global realization of the RRM algorithm is applied to constant pressure auto-ignition and adiabatic premixed laminar flames of hydrogen-air mixtures.

Unstable Manifolds for Partial Functional Differential Equations in Admissible Spaces on the Whole Line

We prove the existence of an unstable manifold for solutions to the partial functional differential equation of the form \(\dot {u}(t)=A(t)u(t)+f(t,u_{t}),~ t\in \mathbb {R}\), under the conditions that the family of linear operators \((A(t))_{t\in \mathbb {R}}\) generates the evolution family (U(t, s))t ≥ s having an exponential dichotomy on the whole line \(\mathbb {R}\), and the nonlinear forcing term f satisfies the φ-Lipschitz condition, i.e., \(\|f(t,\phi ) -f(t,\psi )\| \le \varphi (t)\|\phi -\psi \|_{\mathcal {C}}\) for \(\phi , \psi \in \mathcal {C}:=C([-r, 0], X)\), where φ(⋅) belongs to an admissible function space defined on \(\mathbb {R}\). We also show that such an unstable manifold has the attraction property. Concretely, it attracts exponentially any solution to the abovementioned equation. Our methods are Lyapunov–Perron method combined with the admissibility of function spaces and the technique of choosing induced trajectories.

Analysis of the existence for the steady Navier-Stokes equations with anisotropic diffusion

The boundary-value problem for the generalized Navier-Stokes equations with anisotropic diffusion is considered in this work. For this problem, we prove the existence of weak solutions in the sense that solutions and test functions are considered in the same admissible function space. We also prove the existence of very weak solutions, i.e., solutions for which the test functions have more regularity. By exploiting several examples we show, in the case of dimension $3$, that these existence results improve its isotropic versions in almost all directions or for particular choices of all the diffusion coefficients.

Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions: I

We consider systems of nonautonomous nonlinear differential equations with infinite delay. We introduce Caratheodory type conditions for the right-hand side in an equation, which permit one, on the one hand, to cover a fairly broad class of systems and, on the other hand, include the right-hand side in a compact function space and construct the so-called limiting equations. In the investigation, we use the construction of admissible spaces with fading memory, which permits one to obtain constructive results for the class of equations under study.

Recovering complex elastic scatterers by a single far-field pattern

We consider the inverse scattering problem of reconstructing multiple impenetrable bodies embedded in an unbounded, homogeneous and isotropic elastic medium. The inverse problem is nonlinear and ill-posed. Our study is conducted in an extremely general and practical setting: the number of scatterers is unknown in advance; and each scatterer could be either a rigid body or a cavity which is not required to be known in advance; and moreover there might be components of multiscale sizes presented simultaneously. We develop several locating schemes by making use of only a single far-field pattern, which is widely known to be challenging in the literature. The inverse scattering schemes are of a totally “direct” nature without any inversion involved. For the recovery of multiple small scatterers, the nonlinear inverse problem is linearized and to that end, we derive sharp asymptotic expansion of the elastic far-field pattern in terms of the relative size of the cavities. The asymptotic expansion is based on the boundary-layer-potential technique and the result obtained is of significant mathematical interest for its own sake. The recovery of regular-size/extended scatterers is based on projecting the measured far-field pattern into an admissible solution space. With a local tuning technique, we can further recover multiple multiscale elastic scatterers.

Multiple model-informed open-loop control of uncertain intracellular signaling dynamics.

Computational approaches to tune the activation of intracellular signal transduction pathways both predictably and selectively will enable researchers to explore and interrogate cell biology with unprecedented precision. Techniques to control complex nonlinear systems typically involve the application of control theory to a descriptive mathematical model. For cellular processes, however, measurement assays tend to be too time consuming for real-time feedback control and models offer rough approximations of the biological reality, thus limiting their utility when considered in isolation. We overcome these problems by combining nonlinear model predictive control with a novel adaptive weighting algorithm that blends predictions from multiple models to derive a compromise open-loop control sequence. The proposed strategy uses weight maps to inform the controller of the tendency for models to differ in their ability to accurately reproduce the system dynamics under different experimental perturbations (i.e. control inputs). These maps, which characterize the changing model likelihoods over the admissible control input space, are constructed using preexisting experimental data and used to produce a model-based open-loop control framework. In effect, the proposed method designs a sequence of control inputs that force the signaling dynamics along a predefined temporal response without measurement feedback while mitigating the effects of model uncertainty. We demonstrate this technique on the well-known Erk/MAPK signaling pathway in T cells. In silico assessment demonstrates that this approach successfully reduces target tracking error by 52% or better when compared with single model-based controllers and non-adaptive multiple model-based controllers. In vitro implementation of the proposed approach in Jurkat cells confirms a 63% reduction in tracking error when compared with the best of the single-model controllers. This study provides an experimentally-corroborated control methodology that utilizes the knowledge encoded within multiple mathematical models of intracellular signaling to design control inputs that effectively direct cell behavior in open-loop.

Error Estimate of Eigenvalues of Perturbed Higher-Order Discrete Vector Boundary Value Problems

This paper is concerned with the eigenvalues of perturbed higher-order discrete vector boundary value problems. A suitable admissible function space is first introduced, a new variational formula of eigenvalues is then established under certain nonsingularity conditions, and error estimates of eigenvalues of problems with small perturbation are finally given by using the variational formula. As a direct consequence, continuous dependence of eigenvalues on boundary value problems is obtained under the nonsingularity conditions. In addition, two special perturbed cases are discussed.

ON THE ADMISSIBILITY OF THE SPACE L0($\mathcal{A}$,X) OF VECTOR-VALUED MEASURABLE FUNCTIONS

We prove the admissibility of the space L0(A,X) of vector- valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets. The notion of admissibility introduced by Klee (7) guarantees that a com- pact mapping into an admissible Hausdorff topological vector space E can be approximated by compact finite dimensional mappings. This notion is very important in degree theory and fixed point theory. It is known that locally convex spaces are admissible (see (10)). There are some classes of nonlocally convex spaces which are admissible. Riedrich in (13) proved the admissibility of the space S(0,1) of measurable functions and in (12) the admissibility of the space Lp(0,1) for 0 < p < 1. The admissibility of other function spaces has been proved by Mach (6) and Ishii (8). In (14) it is proved the admissibility of spaces of Besov-Triebel-Lizorkin type. Definition 1 ((7)). Let E be a Haudorff topological vector space. A subset Z of E is said to be admissible if for every compact subset K of Z and for every neighborhood V of zero in E there exists a continuous mapping H : K → Z such that dim(span (H(K)))< +∞ and x−Hx ∈ V for every x ∈ K. If Z = E we say that the space E is admissible. In this paper we deal with spaces of vector-valued measurable functions and, as a major fact, instead of σ-additive measures we consider finitely additive set functions defined on algebras of sets. Let X be a Banach space, a nonempty set, A a subalgebra of the power set P() of and µ : A → R a finitely additive set function. We prove

Integral manifolds for partial functional differential equations in admissible spaces on a half-line

In this paper we investigate the existence of stable and center-stable manifolds for solutions to partial functional differential equations of the form u˙(t)=A(t)u(t)+f(t,ut), t⩾0, when its linear part, the family of operators (A(t))t⩾0, generates the evolution family (U(t,s))t⩾s⩾0 having an exponential dichotomy or trichotomy on the half-line and the nonlinear forcing term f satisfies the φ-Lipschitz condition, i.e., ‖f(t,ut)−f(t,vt)‖⩽φ(t)‖ut−vt‖C where ut,vt∈C:=C([−r,0],X), and φ(t) belongs to some admissible function space on the half-line. Our main methods invoke Lyapunov–Perron methods and the use of admissible function spaces.

The dynamic optimization approach to locomotion dynamics: human-like gaits from a minimally-constrained biped model

This work presents a unifying framework to study energy-efficient optimal gaits for a bipedal model without elastic elements. The model includes a torso, flat feet, and telescoping legs, equipped with rotational hip and ankle joints. Two general types of gaits are studied: with and without a flight phase. The support surface can be level ground, sloped, or staircase. The algorithm achieves the optimum within the admissible space by using a minimal set of realistic physical constraints, and avoiding a priori assumptions on kinetic and kinematic parameters such as extended or instantaneous double-support, collisional or collisionless foot-ground contact, step length, step period, etc. The gait optimization for this simple model predicts many features of human locomotion including the optimality of pendular walking and impulsive running at slow and fast progression speeds, ankle push-off prior to touch-down, swing leg retraction, landing on a near vertical leg in gaits with flight phase, and burst hip torques at both ends of the swing phase.

Single (anti-)top quark production in association with a lightest neutralino at the LHeC

In this paper we examine thoroughly the single (anti-)top quark production associated with a lightest neutralino at the possible CERN Large Hadron Electron Collider. We calculate the full next-to-leading order (NLO) QCD corrections to the process, including all the nonresonant diagrams, and do not assume the production and decay factorization for the possible resonant top squarks in the $R$-parity violating minimal supersymmetric standard model with 19 unrelated parameters. We investigate numerically the effects of the relevant supersymmetry parameters on the cross section, and present the transverse momentum distributions of the final (anti-)top quark at both the leading order (LO) and the QCD NLO. We find that the NLO QCD corrections enhance the LO cross sections in most chosen parameter space, and the NLO QCD impacts on the transverse momentum distributions of the final (anti-)top quark might be resolvable in some cases. We conclude that even with recently known experimental constraints on the supersymmetry parameters, the production rate could still achieve notable value in the admissible parameter space.

Lie-group interpolation and variational recovery for internal variables

We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective is to perform the recovery with minimum error and at the same time guarantee that the internal variables remain in their admissible spaces. The minimization of the error is achieved by a three-field finite element formulation. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an $$L_2$$ L 2 projection that minimizes the distance between the source and target internal variables as measured in the $$L_2$$ L 2 norm of the internal variable space. To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space.

A novel method for prediction of mobile robot maneuvering spaces

As the operational uses of mobile robots continue to expand, it becomes useful to be able to predict the admissible maneuvering space to prevent the robot from executing unsafe maneuvers. A novel method is proposed to address this need by using force–moment diagrams to characterize the robot’s maneuvering space in terms of path curvature and curvature rate. Using the proposed superposition techniques, these diagrams can then be transformed in real-time to provide a representation of the permissible maneuvering space while allowing for changes in the robot’s loading and terrain conditions. Simulation results indicate that the technique can be applied to determine the appropriate maneuvering space for a given set of loading conditions, longitudinal acceleration, and tire–ground coefficient of friction. This may lead to potential expansion in the ability to integrate predictive vehicle dynamics into autonomous controllers for mobile robots and a corresponding potential to safely increase operating speeds.

LEBESGUE COVERING LEMMA ON NONMETRIC SPACES

In this paper the Lebesgue covering lemma is extended from the setting of metric spaces to the setting of admissible spaces. An admissible space is a topological space endowed with an admissible family of open coverings, and need not be metric. The paper contains applications to uniform continuity and dimension theory.

Higgs to μ∓τ± decay in supersymmetry without R-parity

In this letter, we report on lepton flavor violating Higgs decay into μ∓τ± in the framework of the generic supersymmetric standard model without R-parity and list interesting combinations of R-parity violating parameters. We impose other known experimental constraints on the parameters of the model and show our results from the R-parity violating parameters. In our analysis, the branching ratio of can exceed 10−5 within admissible parameter space.

The image of Colmez’s Montreal functor

We prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in irreducible admissible unitary p-adic Banach space representations of GL2(Q p ) with p≥5. This enables us to restate nicely the p-adic local Langlands correspondence for GL2(Q p ) and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.

Comprehensive analysis on lepton flavor violating Higgs boson toμ∓τ±decay in supersymmetry withoutRparity

In this paper we examine thoroughly the Higgs boson to mu tau decay via processes involving R parity violating couplings. By means of full one-loop diagrammatic calculations, we found that even if known experimental constraints, particularly including the stringent sub-eV neutrino mass bounds, give strong restrictions on some of the R parity violating parameters, the branching ratio could still achieve notable value in the admissible parameter space. Hence, the flavor violating leptonic decay is of interest to future experiments. We present here key results of our analysis. Based on the analysis, we give some comments on h -> e mu and h -> e tau also.

Admissibly inertial manifolds for a class of semi-linear evolution equations

Consider the semi-linear evolution equation du(t)dt+Au(t)=f(t,u). We prove the existence of a new class of inertial manifolds called admissibly inertial manifolds for this equation. These manifolds are constituted by trajectories of the solutions belonging to rescaledly admissible function spaces which contain wide classes of function spaces like weighted Lp-spaces, the Lorentz spaces Lp,q and many other rescaling function spaces occurring in interpolation theory. The existence of these manifolds is obtained in the case that the partial differential operator A is positive definite and self-adjoint with a discrete spectrum, and the nonlinear forcing term f satisfies the φ-Lipschitz conditions on the domain D(Aθ), 0⩽θ<1, i.e., ‖f(t,x)−f(t,y)‖⩽φ(t)‖Aθ(x−y)‖ and ‖f(t,x)‖⩽φ(t)(1+‖Aθx‖) for φ(⋅) being a real and positive function which belongs to certain classes of admissible function spaces.

Inertial manifolds for retarded second order in time evolution equations in admissible spaces

Inertial manifolds for retarded second order in time evolution equations in admissible spaces