A model for two-dimensional (2D) quantum gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R) generators) lose their dynamical content (they are no longer conjugated operators). The notion of spacetime itself in 2D gravity then arises as asso...

BACKGROUND Renal failure in neonates is associated with an increased risk of mortality and morbidity. But critical values are not known. OBJECTIVE To define critical values for serum creatinine levels by gestational age in preterm infants, as a predictive factor for mortality and morbidity. STUDY DESIGN This was a retrospective study of all preterm infants born before 33 weeks of gestationa...

Suppose that p ≥ 5 is prime, that F(z) ∈ S2k(Γ0(p)) is a newform, that v is a prime above p in the field generated by the coefficients of F , and that D is a fundamental discriminant. We prove non-vanishing theorems modulo v for the twisted central critical values L(F⊗χD, k). For example, we show that if k is odd and not too large compared to p, then infinitely many of these twisted L-values ar...

To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, in finite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are ...

Many shapes resulting from important geometric operations in industrial applications such as Minkowski sums or volume swept by a moving object can be seen as the projection of higher dimensional objects. When such a higher dimensional object is a smooth manifold, the boundary of the projected shape can be computed from the critical points of the projection. In this paper, using the notion of po...

Tests of statistical hypotheses can be based on either of two critical values: the Type I critical value or the size-corrected critical value. The former usually depends on unknown population parameters and cannot be evaluated exactly in applications, but it can often be estimated very accurately by using the bootstrap. The latter does not depend on unknown population parameters but is likely t...

We study the number ♯ n of real rational degree n functions (considered up to a linear fractional transformation of the independent variable) with a given set of 2n − 2 distinct real critical values. We present a combinatorial interpretation of these numbers and pose a number of related questions.

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any suba...

in this study, the process-based watershed model, soil and water assessment tool (swat), was used for simulating hydrology and sediment transport in the gharesou watershed and for identifying critical areas of soil erosion and water pollution. after model calibration and uncertainty analysis using sufi-2 (sequential uncertainty fitting, ver. 2) method, the outputs of the calibrated model were u...