Weak Convergence and Characteristic Functions

2000 ◽  
pp. 163-167
Author(s):  
Jean Jacod ◽  
Philip Protter
Keyword(s):  
Weak Convergence ◽  
Characteristic Functions

Weak Convergence of Distributions

2021 ◽  
pp. 495-519
Author(s):  
James Davidson
Keyword(s):  
Weak Convergence ◽  
Representation Theorem ◽  
Stable Distribution ◽  
Characteristic Functions ◽  
Random Sums ◽  
Skorokhod Representation Theorem

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved and the chapter then considers the preservation of weak convergence under transformations. Next, the role of moments and characteristic functions is considered. In the leading case of random sums, the criteria for weak convergence and the concept of a stable distribution are studied.

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

scholarly journals Micro-CT and Microscopy Study of Internal and Marginal Gap to Tooth Surface of Crenelated versus Conventional Dental Indirect Veneers

Medicina ◽  
2021 ◽  
Vol 57 (8) ◽  
pp. 772
Author(s):  
Alexandra-Cristina Măroiu ◽  
Cosmin Sinescu ◽  
Virgil-Florin Duma ◽  
Florin Topală ◽  
Anca Jivănescu ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Tooth Surface ◽  
Characteristic Functions ◽  
The Novel ◽  
Micro Ct ◽  
Marginal Gap ◽  
Luting Cement ◽  
Computer Aided ◽  
Internal Adaptation ◽  
Internal Gap

1. Background and Objectives: Ceramic veneers represent the most appropriate treatment option for minimally invasive aesthetic rehabilitation. For long-term clinical success, the accurate marginal and internal adaptation of dental restorations are of paramount importance. The aim of this in vitro study is to assess the effect of a novel (patented) design of veneers compared to conventional ones on their marginal and internal gap to the prepared tooth surface. 2. Materials and Methods: Twenty-four lithium disilicate ceramic veneers are obtained using Computer-Aided-Design (CAD) and then milled using Computer-Aided-Manufacturing (CAM). The samples are divided into two groups: 12 conventional (CO) veneers (i.e., with a linear marginal contour) and 12 crenelated (CR) veneers, the latter with the novel sinusoidal marginal design. All samples are bonded to frontal teeth, and the adhesive interfaces are analyzed using two methods, optical microscopy and micro-Computed Tomography (CT): the former for the accuracy of the marginal gap and the latter for the internal gap (as well as for the homogeneity of the luting cement) of ceramic veneers. 3. Results: STATA and one-way ANOVA tests reveal significant differences between CO and CR veneers: (i) the marginal gap is smaller for CR (64 μm) than for CO veneers (236 μm); (ii) the internal adaptation is better for CR veneers: for a cement width of up to 120 μm, the covered surface for the CR group is 81.5%, while for the CO group it is 64.5%; (iii) the mean of the porosities within the cement is not significantly different (3.4 × 106 μm3 for CO and 3.9 × 106 μm3 for CR veneers), with a higher standard deviation for the CO group. Analytical modeling is achieved for internal gaps using the micro-CT results. The characteristic functions obtained allow us to compare the volume of luting cement for the two types of veneers. 4. Conclusion: The novel veneers design produces an improvement in the marginal and internal adaptation of the restorations to the prepared tooth surface. Thus, it provides favorable premises for better clinical performances.

scholarly journals The Role of Neuropeptide Y in the Nucleus Accumbens

2021 ◽  
Vol 22 (14) ◽  
pp. 7287
Author(s):  
Masaki Tanaka ◽  
Shunji Yamada ◽  
Yoshihisa Watanabe
Keyword(s):  
Nervous System ◽  
Nucleus Accumbens ◽  
Neuropeptide Y ◽  
Emotional Behavior ◽  
Characteristic Functions ◽  
Receptor Subtypes ◽  
Neuroendocrine Mechanisms ◽  
Fear And Anxiety ◽  
The Brain

Neuropeptide Y (NPY), an abundant peptide in the central nervous system, is expressed in neurons of various regions throughout the brain. The physiological and behavioral effects of NPY are mainly mediated through Y1, Y2, and Y5 receptor subtypes, which are expressed in regions regulating food intake, fear and anxiety, learning and memory, depression, and posttraumatic stress. In particular, the nucleus accumbens (NAc) has one of the highest NPY concentrations in the brain. In this review, we summarize the role of NPY in the NAc. NPY is expressed principally in medium-sized aspiny neurons, and numerous NPY immunoreactive fibers are observed in the NAc. Alterations in NPY expression under certain conditions through intra-NAc injections of NPY or receptor agonists/antagonists revealed NPY to be involved in the characteristic functions of the NAc, such as alcohol intake and drug addiction. In addition, control of mesolimbic dopaminergic release via NPY receptors may take part in these functions. NPY in the NAc also participates in fat intake and emotional behavior. Accumbal NPY neurons and fibers may exert physiological and pathophysiological actions partly through neuroendocrine mechanisms and the autonomic nervous system.

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document