Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach

Integral representation is one of the powerful tools for studying analytic continuation of the zeta functions. It is known that Hurwitz zeta function generalizes the famous Riemann zeta function which plays an important role in analytic number theory. They both have several multiple versions in the literature. In this paper, we introduce three novel multiple zeta functions for Barnes type and study their integral representations through hyperbolic probability distributions given by Pitman and Yor (2003, Canad. J. Math., 55, 292-330). The analytically continued properties of the three multiple zeta functions are also investigated. Surprisingly, two of them, unlike the previous results, can extend analytically to entire functions in the whole complex plane.Comment: 20 page

Characterization of Probability Distributions via Functional Equations of Power-Mixture Type

We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations of the type Z = X + TZ, where T is a known random variable, while the variable Z is defined via X, and we want to `find' X. We provide necessary and sufficient conditions for such functional equations to have unique solutions. The uniqueness is equivalent to a characterization property of a probability distribution. We present results which are either new or extend and improve previous results about functional equations of compound-exponential and compound-Poisson types. In particular, we give another affirmative answer to a question posed by J. Pitman and M. Yor in 2003. We provide explicit illustrative examples and deal with related topics.Comment: 28 page

On the second order of Zeta functional equations for Riemann Type

This paper discuss a new class of functional equations by using both Poisson summation formula and Jacobi type theta a function. The class of Riemann type functional equations are derived from self-reciprocal probability density functions. Finally, the second order Zeta functional equations for Riemann type is also investigated.Comment: 13 page

Dynamic Finite Element Analysis on Underlay Microstructure of Cu/low-k Wafer during Wirebonding

The aim of present research is to investigate dynamic stress analysis for microstructure of Cu/Low-K wafer subjected to wirebonding predicted by finite element software ANSYS/LS-DYNA. Two major analyses are conducted in the present research. In the first, the characteristic of heat affected zone (HAZ) and free air ball (FAB) on ultra thin Au wire have been carefully experimental measured. Secondary, the dynamic response on Al pad/beneath the pad of Cu/low-K wafer during wirebonding process has been successfully predicted by finite element analysis (FEA). Tensile mechanical properties of ultra thin wire before/after electric flame-off (EFO) process have been investigated by self-design pull test fixture. The experimental obtained hardening value has significantly influence on localize stressed area on Al pad. This would result in Al pad squeezing around the smashed FAB during impact stage and the consequent thermosonic vibration stage. Microstructure of FAB and HAZ are also carefully measured by micro/nano indentation instruments. All the measured data serves as material inputs for the FEA explicit software ANSYS/LS-DYNA. Because the crack of low-k layer and delamination of copper via are observed, dynamic transient analysis is performed to inspect the overall stress/strain distributions on the microstructure of Cu/low-k wafer. Special emphasizes are focused on the copper via layout and optimal design of Cu/low-k microstructure. It is also shown that the Al pad can be replaced by Al-Cu alloy pad or Cu pad to avoid large deformation on pad and cracking beneath the surface. A series of comprehensive experimental works and FEA predictions have been performed to increase bondability and reliability in this study

Characterization of Probability Distributions via Functional Equations of Power-Mixture Type

We study power-mixture type functional equations in terms of Laplace–Stieltjes transforms of probability distributions on the right half-line [0,∞). These equations arise when studying distributional equations of the type Z=dX+TZ, where the random variable T≥0 has known distribution, while the distribution of the random variable Z≥0 is a transformation of that of X≥0, and we want to find the distribution of X. We provide necessary and sufficient conditions for such functional equations to have unique solutions. The uniqueness is equivalent to a characterization property of a probability distribution. We present results that are either new or extend and improve previous results about functional equations of compound-exponential and compound-Poisson types. In particular, we give another affirmative answer to a question posed by J. Pitman and M. Yor in 2003. We provide explicit illustrative examples and deal with related topics

Neutralization of terminal differentiation in gliomagenesis

An immature state of cellular differentiation - characterized by stem cell-like tendencies and impaired differentiation - is a hallmark of cancer. Using glioblastoma multiforme (GBM) as a model system, we sought to determine whether molecular determinants that drive cells toward terminal differentiation are also genetically targeted in carcinogenesis and whether neutralizing such genes also plays an active role to reinforce the impaired differentiation state and promote malignancy. To that end, we screened 71 genes with known roles in promoting nervous system development that also sustain copy number loss in GBM through antineoplastic assay and identified A2BP1 (ataxin 2 binding protein 1, Rbfox1), an RNA-binding and splicing regulator that is deleted in 10% of GBM cases. Integrated in silico analysis of GBM profiles to elucidate the A2BP1 pathway and its role in glioma identified myelin transcription factor 1-like (Myt1L) as a direct transcriptional regulator of A2BP1. Reintroduction of A2BP1 or Myt1L in GBM cell lines and glioma stem cells profoundly inhibited tumorigenesis in multiple assays, and conversely, shRNA-mediated knockdown of A2BP1 or Myt1L in premalignant neural stem cells compromised neuronal lineage differentiation and promoted orthotopic tumor formation. On the mechanistic level, with the top-represented downstream target TPM1 as an illustrative example, we demonstrated that, among its multiple functions, A2BP1 serves to regulate TPM1's alternative splicing to promote cytoskeletal organization and terminal differentiation and suppress malignancy. Thus, in addition to the activation of self-renewal pathways, the neutralization of genetic programs that drive cells toward terminal differentiation may also promote immature and highly plastic developmental states that contribute to the aggressive malignant properties of GBM

Screening for fear of cancer recurrence : instrument validation and current status in early stage lung cancer patients

Background Fear of cancer recurrence (FCR) is one of the most distressing concerns for cancer patients. A psychometrically validated brief scale is urgently needed for use in busy clinical oncology settings. This study aimed to (1) develop and validate the 7-item fear of cancer recurrence scale Chinese version (FCR7-C), and (2) explore the severity of FCR in post-operative early-stage lung cancer patients in Taiwan. Methods Early-stage lung cancer patients were recruited from a medical center in Taiwan. The FCR7-C was evaluated for content and construct validity and internal consistency reliability. Construct validity of FCR7-C was determined by the empirically supported correlation and confirmatory factor analysis (CFA). Results A total of 160 subjects were recruited. The FCR7-C was shown to have satisfactory content validity and internal consistency reliability (Cronbach's α = 0.9). The uni-dimensional structure was confirmed by CFA that showed a good fit for the model. The FCR7-C score correlates positively with the degree of most of the physical symptoms, anxiety, and depression, but correlates negatively with patient age, performance status, and quality of life. We found that 81.9% of patients reported at least some FCR, with a mean FCR severity of 15.18 (SD = 7.78). Conclusion FCR7-C is a brief screening tool with good psychometrics. Patients with early-stage lung cancer still revealed mild to moderate level of FCR. Applying the FCR7-C for to screen cancer patients’ distress and further develop personalized psychological interventions would be strongly suggested.Publisher PDFPeer reviewe