临界h-边-连通图的临界度

图G称为k-临界h-边-连通的,若h=λ(G)且对每个k顶点集{u1,…,uk}有λ(G-{u1,…,ui})≤λ(G-{u1,…,ui-1})-1,I≤k.若G是k-临界h-边-连通但不(k 1)-临界h-边-连通,则记之为(h*,k*)λ.本文证明了:存在(h*,k*)λ图的充要条件是(1)1≤k≤[(h 1)/2],h≡0,1,2(mod 4);1≤k≤[(h-1)/2],h≡3(mod 4);或(2)k=h,G=Kk 1.     

Elliptic problems with critical exponents and Hardy potentials

This paper is devoted to the existence of positive solutions of a Dirichlet problem with critical exponent and a singular potential. Under various assumption on the domain Ω, which include some kinds of unbounded domains, we prove the existence of ground states and of symmetric solutions.     

A new heuristic for resource-constrained project scheduling in stochastic networks using critical chain concept

This paper presents a newly developed resource-constrained project scheduling method in stochastic networks by merging the new and traditional resource management methods. In each project, the activities consume various types of resources with fixed capacities. The duration of each activity is a random variable with a given density function. Since the backward pass method is implemented for feeding-in resources. The problem is to determine the finish time of each activity instead of its start time. The objective of the presented model is defined as minimizing the multiplication of expected project duration and its variance. The values of activities finish times are determined at decision points when at least one activity is ready to be operated and there are available resources. If at a certain point of time, more than one activity is ready to be operated but available resources are lacking, a competition among ready activities is carried out in order to select the activities which must be operated first. This paper suggests a competition routine by implementing a policy to maximize the total contribution of selected activities in reducing the expected project duration and its variance. In this respect, a heuristic algorithm is developed and compared with the other existing methods.     

Critical features in electromagnetic anomalies detected prior to the L’Aquila earthquake

Earthquakes (EQs) are large-scale fracture phenomena in the Earth’s heterogeneous crust. Fracture-induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. Electromagnetic (EM) emissions in a wide frequency spectrum ranging from kHz to MHz are produced by opening cracks, this can be considered as the so-called precursors of general fracture. We emphasize that the MHz radiation appears earlier than the kHz on both laboratory and geophysical scales. An important challenge in this field of research is to distinguish characteristic epochs in the evolution of precursory EM activity and identify them with the equivalent last stages in the EQ preparation process. Recently, we proposed the following two-stage model. (i) The first epoch, which includes the initial emergent MHz EM emission, is thought to be due to the fracture of a highly heterogeneous system that surrounds a family of large high-strength asperities distributed along the activated fault sustaining the system. (ii) The second epoch, which includes the emergent strong impulsive kHz EM radiation, is due to the fracture of the asperities themselves. A catastrophic EQ of magnitude Mw=6.3 occurred on 6 April, 2009 (06/04/09) in central Italy. The majority of the damage occurred in the city of L’Aquila. Clear kHz–MHz EM anomalies had been detected prior to the L’Aquila EQ. Here, we investigate the seismogenic origin of the MHz part of the anomalies. The analysis, which is in terms of intermittent dynamics of critical fluctuations, reveals that the candidate EM precursor (i) can be described as analogous to a thermal continuous phase transition and (ii) has anti-persistent behavior. These features suggest that this candidate precursor was triggered by microfractures in the highly disordered system that surrounded the backbone of asperities of the activated fault. A criterion for underlying strong critical behavior is introduced. In this field of research, reproducibility of results is desirable; and is best done by analyzing a number of precursory MHz EM emissions. We refer to previous studies of precursory MHz EM activities associated with nine significant EQs that have occurred in Greece in recent years. We conclude that all the MHz EM precursors studied, including the present one, can be described as analogous to a continuous second-order phase transition having strong criticality and anti-persistent behavior.     

Footprints of nonextensive Tsallis statistics, selfaffinity and universality in the preparation of the L’Aquila earthquake hidden in a pre-seismic EM emission

Fracture induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. We investigate the preparation of the recently occurred L’Aquila earthquake in terms of a detected precursory electromagnetic anomaly. The precursor is well described by a recently introduced model for earthquake dynamics, which has been rooted in a nonextensive Tsallis framework starting from first principles. The analysis in terms of nonextensivity implies that the well established aspect of self-affine nature of faulting and fracture is hidden into the precursor, namely, the activation of the L’Aquila fault is a reduced self-affine image of the regional seismicity covering many geological faults. The Gutenberg-Richter magnitude-frequency relationship, the best known scaling relation for earthquakes, verifies the results based on nonextensivity. The latter suggests that the activation of the L’Aquila fault is a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we present evidence for universality in magnetic storm, earthquake, and electromagnetic precursor occurrence by means of complexity and nonextensivity.     

Martensitic transformations: from continuum mechanics to spin models and automata

We present a new procedure for the systematic reduction of a continuum theory of martensitic transformations to a spin system whose dynamics can be described by an automaton. Our prototypical model reproduces most of the experimental observations in martensites associated with criticality and power-law acoustic emission. In particular, it explains in a natural way why cyclic training is necessary to reach scale-free behavior.      

Asymptotics and Blow-up for Mass Critical Nonlinear Dispersive Equations

The author considers mass critical nonlinear Schr（o）dinger and Korteweg-de Vries equations.A review on results related to the blow-up of solution of these equations is given.     

Adsorption of toluene, methylcyclohexane and neopentane on silica MCM-41

Adsorption-desorption isotherms of toluene, methylcyclohexane and neopentane were determined on a silica MCM-41 material of pore diameter ∼3.4 nm over the temperature range 258 K to 308 K (278 K for neopentane). The isosteric enthalpies of adsorption were determined from the isotherms at the various temperatures. It was found that the isotherms of toluene and methylcyclohexane have a similar variation with the temperature, exhibiting hysteresis at 268 K and at lower temperature, while the adsorption of neopentane is reversible at all temperatures. The three organic adsorptives interact differently with the silica surface and the isosteric enthalpies of adsorption indicated that methylcyclohexane has the weakest interaction and toluene the strongest. A slight increase in the adsorption enthalpy at the beginning of the capillary condensation step is observed with methylcyclohexane and neopentane but not with toluene.