Characterization of total ill-posedness in linear semi-infinite optimization

This paper deals with the stability of linear semi-infinite programming (LSIP, for short) problems. We characterize those LSIP problems from which we can obtain, under small perturbations in the data, different types of problems, namely, inconsistent, consistent unsolvable, and solvable problems. The problems of this class are highly unstable and, for this reason, we say that they are totally ill-posed. The characterization that we provide here is of geometrical nature, and it depends exclusively on the original data (i.e., on the coefficients of the nominal LSIP problem). Our results cover the case of linear programming problems, and they are mainly obtained via a new formula for the subdifferential mapping of the support function.Research supported by grants: SB2003-0344 form SEUI (MEC), Spain, MTM2005-08572-C03 (01) from MEC (Spain) and FEDER (E.U.), and ACOMP06/117 from Generalitat Valenciana (Spain)

Cyber Security and the Internet of Things : vulnerabilities and Security requirements

The Internet of Things (IoT) enables billions of embedded computing devices to connect to each other. It includes various kinds of devices, e.g., sensors, actuators, RFID tags, or smartphones, which are very different in terms of size, weight, functionality and capabilities. Their success is very noticed and the number of threats and attacks against IoT devices and services are on the increase as well. In IoT, The objects can be discovered, controlled and managed from the Internet. This articulation, which represents a strong point of the IoT, also inherit all the problematic of the security already present in the Internet. The latter rests even with renewed acuteness in this new environment, because of its characteristics special. It is important to analyze how conventional security requirements (CIA, AAA, etc.) as well as those related to respect for privacy can be broken down in this new environment. This paper is an attempt to classify different vulnerabilities, besides analyze and characterize security requirements

One step protocol and green synthesis of 2-N,N-dimethylamino-3-alkyl(aryl)-2-oxido-1- hydro-2-benzo[1,3,2]diazaphosphinine-4-one derivatives

ABSTRACT. 2-N,N-dimethylamino-2-oxido-3-alkyl(aryl)-1-hydro-2-benzo[1,3,2]diazaphosphinin-4-one (2) derivatives  are synthesized by one pot reaction by reacting equimolar quantities of anthranilic acid, primary amine, and N,N-dimethylphosphoramic dichloride under reflux of ethanol with good yields. The structure of the compounds were established on the basis of their infrared, nuclear magnetic resonance spectral data (1H NMR, 13C NMR and 31P NMR), mass spectrometry, and elemental analysis.   KEY WORDS: Anthranilic acid, N,N-Dimethylphosphoramic dichloride, Diazaphosphinine Bull. Chem. Soc. Ethiop. 2022, 36(4), 859-864.                                                               DOI: https://dx.doi.org/10.4314/bcse.v36i4.11                                                   &nbsp

Dirac Fermions in Inhomogeneous Magnetic Field

We study a confined system of Dirac fermions in the presence of inhomogeneous magnetic field. Splitting the system into different regions, we determine their corresponding energy spectrum solutions. We underline their physical properties by considering the conservation energy where some interesting relations are obtained. These are used to discuss the reflexion and transmission coefficients for Dirac fermions and check the probability condition for different cases. We generalize the obtained results to a system with gap and make some analysis. After evaluating the current-carrying states, we analyze the Klein paradox and report interesting discussions.Comment: 28 pages, 15 figures. Version to appear in JP

Compaction behavior of binary mixtures

Symposium on Powder Science and Technology - Powders and Sintered Material, Albi, FRANCE, MAY 23-25, 2007International audienceThe compaction behavior of binary mixtures of lactose and a functional excipient containing 98% of microcrystalline cellulose and 2% of silica was investigated by experiment. The densification process and the role of each component in the compaction behavior were examined by analyzing the effect of the composition on the stress transmission to the powder bed in axial (stress transmission) and in radial (stress transfer) directions. Unlike the behavior of a single component where the applied pressure is predominantly transmitted in the axial direction to the powder bed for densification, the increase of the composition of lactose up to 50% in mixtures increases the stress transfer that becomes greater than the stress transmission. However, for the compaction behavior of mixtures with 50% of lactose, two opposite behaviors were found, below and above a pressure around 70 MPa. Die-wall friction showed also a change at this pressure due to a smoothed contact surface with wall. By increasing the composition of lactose (>50%), the behavior of mixtures becomes dominated by the behavior of lactose where the transmission is better than the transfer. This study demonstrates that the analysis of the compaction behavior of mixtures by recording stress transmission, stress transfer and wall friction give pertinent information about the role of each component in the densification and Could be, to a certain extent, help to the selection of excipient for powder formulation

Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new rule for the subdifferential of the sum of two convex functions, which uses a strategy of augmenting the involved functions. The main feature of our analysis is that no continuity-type condition is required. Our approach allows us to unify, recover, and extend different results in the recent literature.Research of the first and the second authors is supported by CONICYT grants, Fondecyt 1150909 and 1151003, Basal PFB-03, and Basal FB003. Research of the second and third authors is supported by MINECO of Spain and FEDER of EU, grant MTM2014-59179-C2-1-P. Research of the third author is also supported by the Australian Research Council: Project DP160100854

Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

We provide a rule to calculate the subdifferential set of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions and does not require any assumption either on the index set on which the supremum is taken or on the involved functions. Some other calculus rules, namely chain rule formulas of standard type, are obtained from our main result via new and direct proofs.Research supported by grants MTM2005-08572-C03 (01) from MEC (Spain) and FEDER (E.U.), ACOMP06/117 and ACOMP/2007/247-292 from Generalitat Valenciana (Spain), and ID-PCE-379 (Romania)