A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.     

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming

In this paper we present augmented Lagrangians for nonconvex minimization problems with equality constraints. We construct a dual problem with respect to the presented here Lagrangian, give the saddle point optimality conditions and obtain strong duality results. We use these results and modify the subgradient and cutting plane methods for solving the dual problem constructed. Algorithms proposed in this paper have some advantages. We do not use any convexity and differentiability conditions, and show that the dual problem is always concave regardless of properties the primal problem satisfies. The subgradient of the dual function along which its value increases is calculated without solving any additional problem. In contrast with the penalty or multiplier methods, for improving the value of the dual function, one need not to take the penalty like parameter to infinity in the new methods. In both methods the value of the dual function strongly increases at each iteration. In the contrast, by using the primal-dual gap, the proposed algorithms possess a natural stopping criteria. The convergence theorem for the subgradient method is also presented.     

Semidilute solution structure of cellulose in an ionic liquid and its mixture with a polar organic co‐solvent studied by small‐angle X‐ray scattering

Structural and thermodynamic properties of cellulose solutions in the ionic liquid 1‐ethyl‐3‐methylimidazolium acetate (EMIMAc) and its binary mixtures with N,N‐dimethyl formamide (DMF) are studied by small‐angle X‐ray scattering (SAXS). These measurements indicate molecular dissolution of the cellulose chains without any significant aggregation. The power–law relationships of the evaluated correlation length and osmotic modulus to concentration exhibit exponents of ?0.76 and 2.06 for EMIMAc and ?0.80 and 2.14 for DMF/EMIMAc solvent mixture, respectively. Thus, these solvents can be considered to be good solvents for cellulose. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 888–894     

The Linear-Array Conjecture in Communication Complexity Is False

linear array network consists of k+1 processors with links only between and (0≤i<k). It is required to compute some boolean function f(x,y) in this network, where initially x is stored at and y is stored at . Let be the (total) number of bits that must be exchanged to compute f in worst case. Clearly, , where D(f) is the standard two-party communication complexity of f. Tiwari proved that for almost all functions and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an infinite family of functions for which is essentially at most . Our construction also leads to progress on another major problem in this area: It is easy to bound the two-party communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are such bounds? We exhibit certain functions, for which the (two-party) communication complexity is twice as large as the best lower bound obtainable this way. Received: March 1, 1996     

Electrospinning of ultrahigh‐molecular‐weight polyethylene nanofibers

The electrospinning method has been employed to fabricate ultrafine nanofibers of ultrahigh‐molecular‐weight polyethylene for the first time with a mixture of solvents of different dielectric constants and conductivities. The possibility of producing highly oriented nanofibers from ultrahigh‐molecular‐weight polymers suggests new ways of fabricating ultrastrong, porous, and single‐component nanocomposite fibers with improved properties. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 766–773, 2007     

Inflationary fallacies

It is proven that the chaotic inflationary scenario is not realistic and in many essential points is false.