Ohno and Zagier (Indag Math 12:483–487, 2001) found that a generating function of sums of multiple polylogarithms can be written in terms of the Gauss hypergeometric function
2
F
1
. As a ...generalization of the Ohno and Zagier formula, Ihara et al. (Can J Math 76:1–17, 2022) showed that a generating function of sums of interpolated multiple polylogarithms of Hurwitz type can be expressed in terms of the generalized hypergeometric function
r
+
1
F
r
. In this paper, we establish
q
- and elliptic analogues of this result. We introduce elliptic
q
-multiple polylogarithms of Hurwitz type and study a generating function of sums of them. By taking the trigonometric and classical limits in the main theorem, we can obtain
q
- and elliptic generalizations of the Ihara, Kusunoki, Nakamura and Saeki formula.
Eisenstein derived addition formulas for the Weierstrass zeta function from the addition formula for the cotangent function and the fact that the Weierstrass zeta function can be represented as an ...infinite sum of the cotangent functions. In this paper, we apply this idea of Eisenstein's to the addition type formula for the double cotangent function, established by the author. We show that the elliptic digamma function, defined by the logarithmic derivative of the elliptic gamma function, satisfies an addition type formula. This formula includes the addition formula for the Weierstrass zeta function, evaluation formulas for the double Eisenstein series introduced by Tsumura and the double shuffle relations for the double Eisenstein series, proved by Gangl-Kaneko-Zagier.
It is known that multiple zeta values whose weight and depth are of opposite parity can be written in terms of multiple zeta values of lower depth. This theorem is called parity result. Multiple zeta ...values are special values of the multiple polylogarithms and the parity result is generalized to functional relations satisfied by the multiple polylogarithms. In this paper, we consider
q
- and elliptic generalizations of the parity result. As a main result of this paper, we establish parity result for functions
L
k
(
a
,
α
;
p
,
q
)
, which can be considered to be common deformations of
q
- and elliptic multiple polylogarithms. By taking the trigonometric and classical limits in the main theorem, we obtain
q
- and elliptic analogues of the parity result.
In this paper, we introduce a generating function of sums of two-parameter deformations of multiple polylogarithms, denoted by Φ
2
(
a
;
p
,
q
), and study a
q
-difference equation satisfied by it. ...We show that this
q
-difference equation can be solved by expanding Φ
2
(
a
;
p
,
q
) into power series of the parameter
p
and then using the method of variation of constants. By letting
p
→
0
in the main theorem, we find that the generating function of sums of
q
-interpolated multiple zeta values can be written in terms of the
q
-hypergeometric function
3
ϕ
2
, which is due to Li-Wakabayashi.
Recently, a highly efficient midrange wireless transfer technology using electromagnetic resonance coupling has been proposed and has received much attention due to its practical range and ...efficiency. The resonance frequency of the resonators changes as the gap between the resonators changes. However, when this technology is applied in the megahertz range, the usable frequency is bounded by the industrial, scientific, and medical (ISM) band. Therefore, to achieve maximum power transmission efficiency, the resonance frequency has to be fixed within the ISM band. In this paper, an automated impedance matching (IM) system is proposed to increase the efficiency by matching the resonance frequency of the resonator pair to that of the power source. The simulations and experiments verify that the IM circuits can change the resonance frequency to 13.56 MHz (in the ISM band) for different air gaps, improving the power transfer efficiency. Experiments also verified that automated IM can be easily achieved just by observing and minimizing the reflected wave at the transmitting side of the system.
Display omitted
•Scaffolds with channels directed differently are fabricated by 3D printing.•Channel direction is a critical parameter for bone regeneration.•Channel connection to the periosteum is ...important for a smooth replacement by bone.•Biaxial channels result in too rapid scaffold resorption and bone disappearance.•Micro/nanopores are insufficient, and channels are necessary for bone regeneration.
Although the channel architecture of a scaffold is critical for bone regeneration, little is known for the channel direction. In this study, four types of carbonate apatite cylindrical scaffolds; scaffolds with biaxial channels (VH-scaffold), with uniaxial vertical channels (V-scaffold), with uniaxial horizontal channels (H-scaffold), and without channels (N-scaffold), were implanted in a rabbit femur defect for 4 and 12 weeks. Although the largest bone was formed 4 weeks post-implantation in the VH-scaffold, newly formed bone disappeared with the scaffold after 12 weeks. Thus, biaxial channels resulted in the rapid dissolution of the scaffold and were counterproductive in long-term bone regeneration. The V-scaffold that had channels connected to the periosteum was gradually resorbed throughout 12 weeks post-implantation. The percentage of mineralized bone in the V-scaffolds was equal to that in the natural bone. The resorption and bone percentage of H-scaffolds that had no channels connected to the periosteum were slower and lower, respectively, than those of V-scaffolds. Thus, channels should be connected to the periosteum to achieve smooth replacement by the new bone. In the N-scaffold, much less bone was formed inside the scaffold. This study contributes to providing a design guide for scaffold development in bone engineering.
Aluminum alloys fabricated by laser powder bed fusion (L-PBF) exhibit anisotropic tensile ductility. To identify microstructural origins in melt-pool (MP) structures (formed by the l-PBF process) ...contributing to the anisotropic ductility, the local strain distribution inside the MP structure in deformation was quantified by a combination of digital image correlation (DIC) strain analysis and in-situ SEM observations of tensile tests. It was found that higher strain was localized in locally coarsened microstructures (softer regions) along melt-pool boundaries (MPBs). The strain localization played a significant role in crack initiation (and propagation) around MPBs, contributing to fracture. The strain localization at MPBs changed depending on the geometrical relation of the MPBs with the loading direction (LD), which was controlled by the LD with respect to the building direction of l-PBF samples. The three-dimensional MPB distribution related to the LD would be responsible for the anisotropic ductility.
Display omitted
PDF
