Behaviour of some Hodge invariants by middle convolution

Following an article of Dettweiler and Sabbah, this article studies the behaviour of various Hodge invariants by middle additive convolution with a Kummer module. The main result gives the behaviour of the nearby cycle local Hodge numerical data at infinity. We also give expressions for Hodge numbers and degrees of some Hodge bundles without making the hypothesis of scalar monodromy at infinity, which generalizes the resultsof Dettweiler and Sabbah.

We extend the middle convolution for monodromy of Fuchsian ordinary differential equations due to Katz to an operation for monodromy of KZ equations. This operation, also called the middle convolution, gives a monodromy of KZ equation obtained by the additive middle convolution. Since the fundamental group of the domain of definition of KZ equation is the pure braid group, our middle convolution also gives a recursive way of constructing irreducible representations of the pure braid group. Several applications are considered.

We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.

Comparative assessment of time series and artificial intelligence models to estimate monthly streamflow: A local and external data analysis approach

Forecasting stream flow is a very importance issue in water resources planning and management. The ability of three soft computing methods, least square support vector machine (LSSVM), fuzzy genetic algorithm (FGA) and M5 model tree (M5T), in forecasting daily and monthly stream flows of poorly gauged mountainous watershed using nearby hydro-meteorological data is investigated in the current study. In the first application, monthly stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. LSSVM provides slightly better forecasts than the FGA and M5T models. Stream flow and temperature inputs generally give better forecasts compared to other inputs. In the second application, daily stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. Better results are obtained from the models comprising only stream flow inputs. In general, a better accuracy is obtained from LSSVM models in relative to the FGA and M5T. The results indicate that the monthly and daily stream flows of Hunza can be accurately forecasted by using only nearby climatic data. In the third application, daily stream flows of Hunza river are forecasted using local stream flow and climatic data and the models’ accuracy is slightly increased in relative to the previous applications. LSSVM generally performs superior to the FGA and M5T in forecasting daily stream flow of Hunza river using local stream flow and climatic inputs.

We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds Ω ge that undergo conic degeneration, i.e., that converge in a particular way to a manifold with a conical singularity. Our main result is an asymptotic formula for the determinant up to terms that vanish as ∈ goes to 0. The proof proceeds in two parts: we study the fine structure of the heat trace on the degenerating manifolds via a parametrix construction, and then use that fine structure to analyze the zeta function and determinant of the Laplacian.

We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori estimates for them. Importantly, to do so, we only impose minimal cancellation conditions on the forcing function. Our main result is that all $L^1\cap L^\infty$ localized initial data produces global solutions of the forced SQG, which converge to the steady states in $L^p(\mathbf R^2), 1<p\leq 2$ as time goes to infinity. This establishes that the steady states serve as one point attracting set. Moreover, by employing the method of scaling variables, we compute the sharp relaxation rates, by requiring slightly more localized initial data.

Editorial Introduction D. Alpay, P. Loubaton The tangential trigonometric moment problem on an interval and related topics 1. Introduction 2. Some lemmas on matrix-valued rational functions 3. The main result 4. The Nevanlinna Pick problem References. M. Bakonyi, V.G. Kaftal, G. Weiss, H.J. Woerdeman Maximum entropy and joint norm bounds for operator extensions 1. Introduction 2. A sharp bound in the 2 x 2 case 3. The maximum entropy method 4. An application to integral operators References. J.A. Ball, 1. Gohberg, M.A. Kaashoek Bitangential interpolation for input-output operators of time varying systems: the discrete time case 0. Introduction 1. Residue calculus and generalized point evaluation 2. Pairs of diagonal operators and homogeneous one-sided interpolation 3. Bitangential interpolation data set 4. Bitangential interpolation in geometric terms 5. Intermezzo about admissible Sylvester data sets 6. Construction of a particular solution 7. Parametrization of all solutions (without norm constraints) 8. Input-output operators of time-varying systems 9. Parametrization of all contractive input-output operators satisfying the bitangential interpolation conditions References. J.A.Ball, I.Gohberg, L. Rodman Two-sided tangential interpolation of real rational matrix functions 1. Introduction 2. Minimal realizations 3. Local data 4. Two-sided tangential interpolation: existence of real interpolants 5. Two-sided tangential interpolation with real-valued data: Description of interpolants 6. Degrees of interpolants 7. Generalized Nevanlinna-Pick interpolation for real rational matrix functions References. H. Du, C. Gu On the spectra of operator completion problems 1. Introduction 2. Case of finite dimensional spaces 3. Case of infinite dimensional spaces References. C. Foias, A.E. Frazho, W.S. Li The exact H2 estimate for the central H interpolant Introduction 1. An improved Kaftal-Larson-Weiss estimate 2. Some formulas for DB 3. The role of DA2II0 4. The four block problem 5. Optimal solutions References. A.E. Frazho, S.M. Kherat On mixed H2 - H tangential interpolation 1. Introduction 2. Formulas for the central solution 3. A state space approach 4. Applications of the H2-H tangential interpolation problem References. I. Gohberg, C. Gu On a completion problem for matrices 1. Introduction 2. Main theorems in the finite dimensional case 3. The full range case 4. The proof of the main theorems in the finite dimensional case 5. Infinite dimensional case References.

Full assessment energy-sources for inclusive energy-resources planning

Climatic risk in crop production: Models and management for the semiarid tropics and subtropics: R.C. Muchow and J.A. Bellamy (Editors), 1991. 548 pp., £49.50/US$94.00, ISBN 0-85198-665-X

We have three main results. First, we show that a smooth complex projective variety which contains three disjoint codimension-one subvarieties in the same homology class must be the union of a whole one-parameter family of disjoint codimension-one subsets. More precisely, the variety maps onto a smooth curve with the three given divisors as fibers, possibly multiple fibers (Theorem 2.1). The beauty of this statement is that it fails completely if we have only two disjoint divisors in a homology class, as we will explain. The result seems to be new already for curves on a surface. The key to the proof is the Albanese map. We need Theorem 2.1 for our investigation of a question proposed by Fulton, as part of the study of degeneracy loci. Suppose we have a line bundle on a smooth projective variety which has a holomorphic section whose divisor of zeros is smooth. Can we compute the Betti numbers of this divisor in terms of the given variety and the first Chern class of the line bundle? Equivalently, can we compute the Betti numbers of any smooth divisor in a smooth projective variety X in terms of its cohomology class in H2(X,Z)? The point is that the Betti numbers (and Hodge numbers) of a smooth divisor are determined by its cohomology class if the divisor is ample or if the first Betti number of X is zero (see section 4). We want to know if the Betti numbers of a smooth divisor are determined by its cohomology class without these restrictions. The answer is no. In fact, there is a variety which contains two homologous smooth divisors, one of which is connected while the other is not connected. Fortunately, we can show that this is a rare phenomenon: if a variety contains a connected smooth divisor which is homologous to a non-connected smooth divisor, then it has a surjective morphism to a curve with some multiple fibers, and the two divisors are both unions of fibers. This is our second main result, Theorem 5.1. We also give an example of two connected smooth divisors which are homologous but have different Betti numbers. Conjecture 6.1, suggested by this example, asserts that two connected smooth divisors in a smooth complex projective variety X which are homologous should have cyclic etale coverings which are deformation equivalent to each other. The third main result of this paper, Theorem 6.3, is that this conjecture holds, in a slightly weaker form (allowing deformations into positive characteristic), under the strange assumption that the Picard variety of X is isogenous to a product of elliptic curves. The statement in general would follow from a well-known open problem in the arithmetic theory of abelian varieties, Conjecture 6.2: for any abelian variety A over a number field F , there are infinitely many primes p of the ring of integers oF such that the finite group A(oF /p) has order prime to the characteristic of the field oF /p.

&amp;lt;p&amp;gt;River runoff prediction plays a very vital role in water resources planning, hydropower designing and agricultural water management. In the current study, the prediction capability of three machine learning models, least square support vector regression (LSSVR), fuzzy genetic (FG) and M5 model tree (M5Tree), in modeling daily and monthly runoffs of Hunza River catchment (HRC) using own and nearby Gilgit climatic station data is examined. The prediction performances of three machine learning models are compared using three statistical indexes, namely, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;). Firstly, four previous time lagged values of runoff, rainfall and atmospheric temperature are used as inputs on basis of correlation analysis to validate and test the accuracy of three machine learning models. After analyzing the performance of various input combinations, optimal one is selected for each variable and then these optimal inputs are employed together to see the forecasting performance. In the first part of study, monthly runoff of HRC are predicted using inputs consisting of local previous monthly runoff values and monthly meteorological values of Gilgit station. The test results show that LSSVR provides more accurate prediction results than the other two machine learning models. In the second part, daily runoffs of HRC are predicted using own previous daily runoff and Gilgit station&amp;amp;#8217;s climatic values. In the test results, a better accuracy is obtained from LSSVR models in relative to the FG and M5Tree models. In the last part of study, daily runoffs of HRC are predicted using own runoff and climatic data of HRC. In the results, it is found that local climatic data slightly improved the all model&amp;amp;#8217;s prediction accuracy in comparison of other scenario which also uses nearby station&amp;amp;#8217;s climatic data. The LSSVR models again are found to be better than the FGA and M5Tree models. LSSVM generally performs superior to the FGA and M5Tree in forecasting daily stream flow of Hunza River using local stream flow and climatic inputs. Based on the results of study, LSSVR model is recommended for monthly and daily runoff prediction of HRC with or without local climatic data.&amp;lt;/p&amp;gt;

Chapter 6: Middle additive convolution

&lt;p&gt;The paper describes the final results of the project focused on the assessment of the existing railway bridges with respect to the wind load and traffic load in both ultimate limit state and equilibrium limit state. The outcomes of the project are based on extensive wind tunnel testing. Detailed probabilistic and reliability study is presented in this contribution using the wind tunnel data, and available railway traffic and wind speed data for a given location. The main result is a set of reduction factors for wind forces acting on specific railway bridge types and rail vehicles and calibrated combination factors for simultaneous action of unloaded train and wind in equilibrium limit state.&lt;/p&gt;

We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R. Schul in Euclidean space, for an arbitrarylocally finite Borel measurein an arbitraryCarnot group, we develop tests that identify the part of the measure that is carried by rectifiable curves and the part of the measure that is singular to rectifiable curves. Our main result is entwined with an extension ofanalyst’s traveling salesman theorem, which characterizes the subsets of rectifiable curves inR2{{\mathbb{R}}}^{2}(P. W. Jones,Rectifiable sets and the traveling salesman problem, Invent. Math.102(1990), no. 1, 1–15), inRn{{\mathbb{R}}}^{n}(K. Okikiolu,Characterization of subsets of rectifiable curves inRn{{\bf{R}}}^{n}, J. London Math. Soc. (2)46(1992), no. 2, 336–348), or in an arbitrary Carnot group (S. Li) in terms of local geometric least-squares data calledJones’β\beta-numbers. In a secondary result, we implement the Garnett-Killip-Schul construction of a doubling measure inRn{{\mathbb{R}}}^{n}that charges a rectifiable curve in an arbitrarycomplete, doubling, locally quasiconvex metric space.