This paper presents a UV (ultraviolet) lithography apparatus that utilizes an array composed of UV-LED (light emitting diode) collimation modules as a micro-patterning light source for PCB (printed circuit board) fabrication. To provide a uniform (non-uniformity > 90%) and collimated (FWHM < ±2°) exposure area, hexagonal light source modules are disposed in a hexagonal array. Each module is con...

Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N∗(x) of an element x ∈ N to be bounded by the rank of N . The Generalized Principal Ideal Theorem of Bruns, Eisenbud and Evans says that this inequality always holds if x ∈ mN . We show that the inequality even holds if the hypothesis becomes true after first extending sc...

For groups other than p-groups, some work has been done for general situations [12, 13] and for simple groups [4, 5, 6]. Balmer [2] has made connections with the Picard group of the spectrum of the stable category. Nakano and the author have had some success extending the results to more general finite group schemes. For example, in the case of a p-restricted Lie algebra whose cohomology ring s...

Human motor behavior can be generated using distributed system. In this study, human standing-up motion is focused as an important daily activity. Especially, 13 muscle activation of lower body and trunk during human standing-up motion is decomposed into small numbers of modules of synchronized muscle activation called muscle synergy. Moreover human musculoskeletal model is developed with four ...

High voltage IGBT modules are widely used in high power applications, such as traction and large drives. These applications demand high reliability modules and power devices with improved electrical characteristics in terms of reduced losses, increased ruggedness and good controllability for an increased temperature range. The previous SPT+ 3.3kV module rated at 1500A offered superior static an...

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

We define and study the symmetric version of differential torsion theories. We prove that the symmetric versions of some of the existing results on derivations on right modules of quotients hold for derivations on symmetric modules of quotients. In particular, we prove that the symmetric Lambek, Goldie and perfect torsion theories are differential. We also study conditions under which a derivat...

In floorplanning, it is common that a designer wants to have certain modules abutting with one another in the final packing. The problem of controlling the relative positions of an arbitrary number of modules in floorplan design is nontrivial. Slicing floorplan has an advantageous feature in which the topological structure of the packing can be found without knowing the module dimensions. This ...

 The class of ads modules with the SIP (briefly‎, ‎$SA$-modules) is studied‎. ‎Various conditions for a module to be $SA$-module are given‎. ‎It is proved that for a quasi-continuous module $M$‎, ‎$M$ is a UC-module if and only if $M$ is an $SA$-module‎. ‎Also‎, ‎it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...