Search results for "Uniqueness"
showing 10 items of 211 documents
Green’s function and existence of solutions for a third-order three-point boundary value problem
2019
The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
2004
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
On a possible origin of quantum groups
1991
A Poisson bracket structure having the commutation relations of the quantum group SLq(2) is quantized by means of the Moyal star-product on C∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra Uq(sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of Uq(sl(2)).
Gauge-invariant resummation formalism for two-point correlation functions
1996
The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. A formalism is presented for resummation of off-shell two-point correlation functions, which is mainly based on arguments of analyticity, unitarity, gauge invariance and renormalizability. The analytic results obtained with various methods, including the background field gauges and the pinch technique are confronted with the physical requirements imposed; to one-loop order the pinch technique appr…
Single and Double Beta-DecayQValues among the TripletZr96,Nb96, andMo96
2016
The atomic mass relations among the mass triplet ^{96}Zr, ^{96}Nb, and ^{96}Mo have been determined by means of high-precision mass measurements using the JYFLTRAP mass spectrometer at the IGISOL facility of the University of Jyvaskyla. We report Q values for the ^{96}Zr single and double β decays to ^{96}Nb and ^{96}Mo, as well as the Q value for the ^{96}Nb single β decay to ^{96}Mo, which are Q_{β}(^{96}Zr)=163.96(13), Q_{ββ}(^{96}Zr)=3356.097(86), and Q_{β}(^{96}Nb)=3192.05(16) keV. Of special importance is the ^{96}Zr single β-decay Q value, which has never been determined directly. The single β decay, whose main branch is fourfold unique forbidden, is an alternative decay path to the…
Compartmental analysis of dynamic nuclear medicine data: Models and identifiability
2016
Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied t…
Beyond the triangle and uniqueness relations: non-zeta counterterms at large $N$ from positive knots
1997
Counterterms that are not reducible to ζn are generated by 3F2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N 3) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Pade resummations of e-expansions, which are compared with analytical results in 3 dimensions. The O(1/N 3) results entail knots gener…
Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data
2008
Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.
Asymptotic behaviour of mixed-type circuits. Delay time predicting
1991
In the preceding chapter we have shown that the delay time problem in integrated circuits leads us to consider mixed-type circuits with distributed elements described by Telegraph Equations and lumped resistive and capacitive elements (Figure 4.5). Moreover, the well-posedness of the mathematical model (P(B, V0)) = (E) + (BC) + (IC) has been studied, various conditions for the existence, uniqueness and L2stability of different kind of solutions being formulated.