An efficient numerical method for shakedown analysis

The algorithm proposed in [9] for incremental elastoplasticity is extended and applied to shakedown analysis. Using the three field mixed finite element proposed in [22] a series of mathematical programming problems or steps, obtained from the application of the proximal point algorithm to the static shakedown theorem, are obtained. Each step is solved by an Equality Constrained Sequential Quadratic Programming (EC-SQP) tech- nique that allows a consistent linearization of the equations improving the computational efficiency

A random laser tailored by directional stimulated emission

A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter accounts for this duality with the onset of a mode locked regime in which increasing the number of activated modes results in an increased inter mode correlation and a pulse shortening ascribed to a synchronization phenomenon. An extended discussion of our experimental approach together with an original study of the spatial properties of the RL is reported here.Comment: 9 Pages; 16 Figure

Sums of Multivariate Polynomials in Finite Subgroups

Let R be a commutative ring, f ∈ R[X1,⋯,Xk] a multivariate polynomial, and G a finite subgroup of the group of units of R satisfying a certain constraint, which always holds if R is a field. Then, we evaluate Σ f(x1,⋯,xk), where the summation is taken over all pairwise distinct x1,⋯,xk G. In particular, let ps be a power of an odd prime, n a positive integer coprime with p - 1, and a1,⋯,ak integers such that φ(ps) divides a1 + ⋯ + ak and p - 1 does not divide Σi∈Iai for all non-empty proper subsets I ⊆ {1,⋯,k}; then ∑x1a1⋯xkak ≡ φ(ps)/gcd(n,φ(ps))(-1)k-1(k - 1)!modps, where the summation is taken over all pairwise distinct nth residues x1,⋯,xk modulo ps coprime with p

Density-like and Generalized Density Ideals

We show that there exist uncountably many (tall and nontall) pairwise nonisomorphic density-like ideals on which are not generalized density ideals. In addition, they are nonpathological. This answers a question posed by Borodulin-Nadzieja et al. in [this Journal, vol. 80 (2015), pp. 1268-1289]. Lastly, we provide sufficient conditions for a density-like ideal to be necessarily a generalized density ideal

Expert Opinion Pleading: Any Merit to Special Certificates of Merit?

Civil litigation reform to reduce frivolous civil lawsuits was a hot topic in the most recent Presidential debates. It has stirred much recent interest and action in state and federal legislatures. Some new developments involve special pleading norms. Lawmakers will likely debate and implement new special pleading requirements in coming years, often involving certificates of merit. Such certificates are now required for most or some professional malpractice claims in several states. Illinois adopted a certificate of merit standard for product liability actions, while certificates of merit for certain childhood sexual abuse claims are necessary in both California and Louisiana. As debate continues over the need for and benefits of such special pleading requirements, lawmakers should ensure that empirical evidence supports any new legislation. In implementing new certificates of merit, careful attention must be directed to constitutional issues, as well as to policy questions involving the breadth of coverage, the nature of any needed expert opinion, the opportunity for pre-filing discovery, and the possible sanctions upon noncompliance. Upon reviewing various approaches to the use of special certificates of merit to reduce frivolous lawsuits, certain provisions for any future legislation are recommended to address the problems raised by current statutes. To address ambiguities in the breadth of coverage, certificate of merit requirements should be limited to claims where expert testimony is necessary to establish a prima facie case. Expert opinions should be required only after the initial pleadings have been completed, after there has been some opportunity for discovery, and only when the court deems them necessary. Expert opinions filed only for the purpose of certifying the merits of the civil action should not normally be admissible unless the experts are expected to testify at trial. Most would agree with President Clinton who said in the 1996 Presidential debates that frivolous civil lawsuits should be reduced as long as deserving claimants are also not denied recovery. Easier said than done

Is type 2 diabetes really resolved after laparoscopic sleeve gastrectomy? Glucose variability studied by continuous glucose monitoring

The study was carried out on type 2 diabetic obese patients who underwent laparoscopic sleeve gastrectomy (LSG). Patients underwent regular glycemic controls throughout 3 years and all patients were defined cured from diabetes according to conventional criteria defined as normalization of fasting glucose levels and glycated hemoglobin in absence of antidiabetic therapy. After 3 years of follow-up, Continuous Glucose Monitoring (CGM) was performed in each patient to better clarify the remission of diabetes. In this study, we found that the diabetes resolution after LSG occurred in 40% of patients; in the other 60%, even if they showed a normal fasting glycemia and A1c, patients spent a lot of time in hyperglycemia. During the oral glucose tolerance test (OGTT), we found that 2 h postload glucose determinations revealed overt diabetes only in a small group of patients and might be insufficient to exclude the diagnosis of diabetes in the other patients who spent a lot of time in hyperglycemia, even if they showed a normal glycemia (<140 mg/dL) at 120 minutes OGTT. These interesting data could help clinicians to better individualize patients in which diabetes is not resolved and who could need more attention in order to prevent chronic complications of diabetes

A mixed algorithm for incremental elastoplastic analysis

A new method for the incremental analysis of elastoplastic associated materials is presented. The method fully retains all the equations and variables of the problems at the same level and uses a sequential quadratic programming with equality constraints to solve in an efficient and robust fashion the elastoplastic step equations derived by means of a suitable mathematical programming formulation of the problem. The new proposal is compared with standard strain driven formulations which use a return mapping by closest point projection schemes. The numerical tests performed show a good performance and a great robustness of the proposed formulation also in the case of multi–surface elastoplasticity

Condensation in disordered lasers: theory, 3D+1 simulations and experiments

The complex processes underlying the generation of a coherent-like emission from the multiple-scattering of photons and wave-localization in the presence of structural disorder are still mostly un-explored. Here we show that a single nonlinear Schroedinger equation, playing the role of the Schawlow-Townes law for standard lasers, quantitatively reproduces experimental results and three-dimensional time-domain parallel simulations of a colloidal laser system.Comment: 4 pages, 5 figure