A CLASS OF HOLOMORPHIC DIRICHLET-HURWITZ-LERCH EISENSTEIN SERIES AND RAMANUJAN'S FORMULA FOR SPECIFIC VALUES OF THE RIEMANN ZETA-FUNCTION (Analytic Number Theory and Related Topics)

We show in this paper that complete asymptotic expansions exist for a class of holomorphic Dirichlet-Hurwitz-Lerch Eisenstein series (Theorems 1 and 2), which, together with their remainders in exact form (Theorem 3), naturally transfer to several (additive and multiplicative) character analogues of Ramanujan's formula for specific values of the Riemann zeta-function (Theorem 4 and Corollary 4.1), and further to the (quasi) modular relations for similar character analogues of the classical Eisenstein series with integer weights (Corollary 4.2). Prior to the (sketched) derivation of our main formula, we prepare several basic (but new) results on Dirichlet-Hurwitz-Lerch $L$-functions (Theorems 5, 6 and Lemmas 1-3), which play underlying roles in all aspects of the proofs; the detailed version of the proofs will appear in a forthcoming article [16]

TRANSFORMATION FORMULAE AND ASYMPTOTIC EXPANSIONS FOR DOUBLE HOLOMORPHIC EISENSTEIN SERIES OF TWO COMPLEX VARIABLES (SUMMARIZED VERSION) (Analytic Number Theory : Distribution and Approximation of Arithmetic Objects)

This is a summarized version of the forthcoming paper [10]. The main object of study in [10] is the double holomorphic Eisenstein series overline{$zeta$_{mathrm{Z}^{2}(s;z), defined by (1.10) with (1.9) below, having two complex variables s=(s_{1}, s_{2}) and two parameters z=(z_{1}, z_{2}) satisfying either zin(mathfrak{H}^{+})^{2} or zin(mathfrak{H}^{-})^{2}, for which its transformation properties and asymptotic aspects are studied when the distance |Z2-Z1| becomes small and large under certain natural settings on the movement of zin(mathfrak{H}^{pm})^{2}. Let $epsilon$underline{(w}) be the signature defined by (1.2). We establish in [10] complete asymptotic expansions of $zeta$_{mathbb{Z}^{2}}(s;z) when z moves within either the poly-sector (mathfrak{H}^{+})^{2} or (mathfrak{H}^{-})^{2}, so as that the pivotal parameter $eta$, defined by (1.7) with (1.2) and (1.5), tends to 0 through |arg $eta$|< $pi$/2 in the ascending order of $eta$ (Theorem 1); this further leads us to show that counterpart expansions exist for $zeta$_{mathrm{Z}^{2}}(s;z) in the descending order of $eta$ as $eta$rightarrowinfty through |arg $eta$|< $pi$/2 (Theorem 2). Our second main formula in Theorem 2 naturally reduces to various expressions of overline{$zeta$_{mathrm{Z}^{2}(s;z) (in finitely closed forms) at any integer lattice points sin mathbb{Z}^{2} (Corollaries 2. 1-2.14). A major portion of these results reveals that specific values of overline{$zeta$_{mathbb{Z}^{2}(s;z) at sin mathbb{Z}^{2} are closely linked to WeierstraB elliptic functions $beta$(w|2 $pi$(1, $epsilon$(z_{j})z_{j}))(j=1, 2), the classical Eisenstein senes mathscr{S}_{r}(q_{j}) in (5.9), reformulated by Ramanujan [18], as well as the Jordan-Kronecker type functions $eta$_{mathrm{J}_{1}}(w;q_{j}) and ($rho$_{2}(w;q_{j}) in (5.23), each defined with the distinct bases q_{j}=e($epsilon$(z_{j})z_{J})(j=1, 2), the latter two of which were extensively utilized by Ramanujan in the course of developing his theory of Eisenstein series, elliptic functions and theta functions (cf.[1][2][21]). As for the methods used in [10], crucial rôles are played by a class of Mellin-Uarnes type integrals, manipulated with several properties of confluent hypergeometric functions

High-throughput DBC-assembled IGBT screening for power module

High-throughput DBC-assembled IGBT screening equipment for a production line is under development in order to prevent early failure of power modules. The equipment has been planning to have automatic GO/NO GO judgment technology by high-throughput measurement of current signal distribution with non-contact sensor arrays with small coils over the bonding wires of IGBT chips. Basic technology and Prototypes of a sensor, an analog amplifier, digital compensation technology, a test head and power circuit have been almost completed. The authors will fabricate the sensor arrays and develop GO/NO GO judgement technology with the integration of a basic technology.8th International Conference on Integrated Power Electronics Systems (CIPS 2014), February 25-27, 2014, Nuremberg, German

The relationship between attention and avoidance coping in anorexia nervosa: functional magnetic resonance imaging study

[Background] Numerous studies have demonstrated attentional control difficulties and high avoidance coping in patients with anorexia nervosa. Attention is a critical coping resource because it enables individuals to demonstrate self-control and complete goal-directed behaviours. [Aims] We aimed to examine whether attentional control difficulty is related to high avoidance coping, and investigate the neural underpinnings of attentional control difficulties in individuals with anorexia nervosa. [Method] Twenty-three patients with anorexia nervosa and 17 healthy controls completed questionnaires that assessed attention and coping, and underwent functional magnetic resonance imaging while performing a go/no-go task. [Results] Patients with anorexia nervosa showed weaker attentional control, higher omission error rates and higher avoidance coping compared with healthy controls. Attentional control difficulty was associated with higher avoidance coping in both groups. Functional magnetic resonance imaging analysis showed less deactivation in regions representing internal mental processing, such as the praecuneus, cuneus and left lingual gyrus, during the no-go condition. Moreover, weakened deactivation of the left lingual gyrus was associated with higher commission error rate in the anorexia nervosa group. [Conclusions] Our results suggest that patients with anorexia nervosa may have difficulty in maintaining attention to external ongoing events because of disturbance from internal self-related thought, and support the notion that attentional control difficulties underlie the frequent use of avoidance coping in anorexia nervosa

Neural correlates of a mindfulness-based intervention in anorexia nervosa

神経性やせ症患者の不安に対するマインドフルネス瞑想の効果 --脳活動の変化を明らかに--. 京都大学プレスリリース. 2023-02-02.Accepting anxiety for peace of mind. 京都大学プレスリリース. 2023-02-08.We examined the neural underpinnings of the effects of mindfulness on anxiety in anorexia nervosa using functional magnetic resonance imaging in 21 anorexia patients. We used a functional magnetic resonance imaging task designed to induce weight-related anxiety and asked participants to regulate their anxiety either using or not using an acceptance strategy. Our results showed reduced activity in the amygdala, anterior cingulate cortex, putamen, caudate, orbital gyrus, middle frontal gyrus, posterior cingulate cortex and precuneus following a mindfulness-based intervention. The present study provides new insight regarding the neural mechanisms underlying the effect of mindfulness-based intervention in ameliorating anorexia nervosa