The critical points of the continuous series are characterized by two complex numbers l1,2(Re(l1,2) < 0), and a natural number n(n ≥ 3) which enters the string susceptibility constant through γ = −2 n−1 . The critical potentials are analytic functions with a convergence radius depending on l1 (or l2). We use the orthogonal polynomial method and solve the SchwingerDyson equations with a techniqu...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...

This paper analyzes the scaling window of a random CSP model (i.e. model RB) for which we can identify the threshold points exactly, denoted by rcr or pcr. For this model, we establish the scaling window W (n, δ) = (r − (n, δ), r+(n, δ)) such that the probability of a random instance being satisfiable is greater than 1 − δ for r < r − (n, δ) and is less than δ for r > r+(n, δ). Specifically, we...

The scaling of respiratory metabolism with body size in animals is considered by many to be a fundamental law of nature. An apparent corollary of this law is the scaling of physiologic time with body size, implying that physiologic time is separate and distinct from clock time. However, these are only two of the many allometry relations that emerge from empirical studies in the physical, social...

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi–Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in particular we write down the annulus amplitude in terms of theta functions on a Riemann surface. We test these ideas on local curves and local surfaces, provid...

We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prov...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 &amp; 0 &amp; -11 &amp; 1 &amp; 0 1 &amp;  0 &amp; 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provi...