The Existence and Construction of (K5∖e)‐Designs of Orders 27, 135, 162, and 216

The problem of the existence of a decomposition of the complete graph ey:10638539:media:jcd21340:jcd21340-math-0001" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/d6fc7852-26a2-4447-ab7b-0388b9650a52/jcd21340-math-0001.png"> into disjoint copies of ey:10638539:media:jcd21340:jcd21340-math-0002" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/9074b2e7-9cfc-4c66-90e8-027b5805086e/jcd21340-math-0002.png"> has been solved for all admissible orders n, except for 27, 36, 54, 64, 72, 81, 90, 135, 144, 162, 216, and 234. In this paper, I eliminate 4 of these 12 unresolved orders. Let Γ be a ey:10638539:media:jcd21340:jcd21340-math-0003" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/a61e6418-7e5a-4dea-b2a8-2c025bb1ed46/jcd21340-math-0003.png">‐design. I show that ey:10638539:media:jcd21340:jcd21340-math-0004" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/a8ed2ff0-bd29-4fed-a250-632f8aef179c/jcd21340-math-0004.png"> divides 2^k3 for some ey:10638539:media:jcd21340:jcd21340-math-0005" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/f4ddfec9-7db3-4ab7-bd0e-582b95093971/jcd21340-math-0005.png"> and that ey:10638539:media:jcd21340:jcd21340-math-0006" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/f252b987-f05c-4c1e-a031-be3ffe4227ea/jcd21340-math-0006.png">. I construct ey:10638539:media:jcd21340:jcd21340-math-0007" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/7d6ffd14-136b-4c3c-8887-df2a6684e70a/jcd21340-math-0007.png">‐designs by prescribing ey:10638539:media:jcd21340:jcd21340-math-0008" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/1aee69fe-af32-4924-8ccb-5a574f4f4c71/jcd21340-math-0008.png"> as an automorphism group, and show that up to isomorphism there are exactly 24 ey:10638539:media:jcd21340:jcd21340-math-0009" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/842957cf-160d-45ff-a840-dd2cf8ad6899/jcd21340-math-0009.png">‐designs with ey:10638539:media:jcd21340:jcd21340-math-0010" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/173d172c-ba9c-4ca9-8148-26036172426c/jcd21340-math-0010.png"> as an automorphism group. Moreover, I show that the full automorphism group of each of these designs is indeed ey:10638539:media:jcd21340:jcd21340-math-0011" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/aa34ce76-7813-424d-9b4d-23c6a28303df/jcd21340-math-0011.png">. Finally, the existence of ey:10638539:media:jcd21340:jcd21340-math-0012" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/a9993ac3-c5ea-4ee9-9de1-57fc45570ff6/jcd21340-math-0012.png">‐designs of orders 135, 162, and 216 follows immediately by the recursive constructions given by G. Ge and A. C. H. Ling, SIAM J Discrete Math 21(4) (2007), 851–864.     

Bias voltage effect on electron tunneling across a junction with a ferroelectric-ferromagnetic two-phase composite barrier

The effect of bias voltage on electron tunneling across a junction with a ferroelectric-ferromagnetic composite barrier is investigated theoretically. Because of the inversion symmetry breaking of the spontaneous ferroelectric polarization, bias voltage dependence of the electron tunneling shows significant differences between the positive bias and the negative one. The differences of spin filtering or tunnel magnetoresistance increase with the increasing absolute value of bias voltage. Such direction preferred electron tunneling is found intimately related with the unusual asymmetry of the electrical potential profile in two-phase composite barrier and provides a unique change to realize rectifying functions in spintronics.     

含幺元的半格和群的Zappa-Sz\'{e}p积上的同余

Let P = E G be a Zappa-Szp product of a semilattice E with an identity and a group G. In this paper, we first introduce the concept of congruence pairs for P , and then prove that every congruence on P can be described by such a congruence pair. In fact the congruence lattice on P is lattice-isomorphic to the set of all congruence pairs for P . Finally,we characterize group congruences on P .     

Study of （e, 2e） process on potassium at 6 eV-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation(DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections(TDCS) of coplanar doubly symmetric(e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric(e,2e) problems in low and intermediate energy ranges.     

Fuzzy real valued lacunary I-convergent sequences

In this article, we introduce the concept of lacunary <em>Iem>-convergent sequence of fuzzy real numbers and study some basic properties.     

A note on strong matrix summability via ideals

Following the line of recent works of Das et al. (2011) [15] and Savas and Das (2011) [19] we apply the notion of ideals to strong matrix summability, and in this note, we introduce the notion of strong <em>Aem>^<em>Iem>-summability with respect to an Orlicz function. We make certain investigations on the classes of sequences arising out of this new summability method.     

基态波函数对氦原子双电离微分截面的影响

文中采用氨原子的三种近似波函数,计算了入射电子能量为5599 eV时,敲出电子共面等能分享几何安排下,氦原子双电离He(e,3e)反应全微分截面.结果表明三种波函数的理论计算结果,在误差范围内都与实验数据基本吻合,其中采用Pluvinage波函数所得到的理论数据更接近实验数据.     

Density functional study of the adsorption of aspirin on the hydroxylated (0 0 1) -quartz surface

In this study the adsorption geometry of aspirin molecule on a hydroxylated (0 0 1) α-quartz surface has been investigated using DFT calculations. The optimized adsorption geometry indicates that both, adsorbed molecule and substrate are strongly deformed. Strong hydrogen bonding between aspirin and surface hydroxyls, leads to the breaking of the original hydroxyl–hydroxyl hydrogen bonds (Hydrogenbridges) on the surface. In this case new hydrogen bonds on the hydroxylated (0 0 1) α-quartz surface appear which significantly differ from those at the clean surface. The 1.11 eV adsorption energy reveals that the interaction of aspirin with α-quartz is an exothermic chemical interaction.     

Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders

In this paper, we design resonant reflection grating filters employing the second diffracted orders as the leaky modes, then analyze the bandwidth of the reflection peak and the electric field distributions inside the waveguide under resonance. The numeric calculation confirms that ultra-narrow resonant reflection peaks can be observed in these structures. At the same time, strong electric field enhancement appears under resonance. It provides a new approach to diversify the resonant reflection filters and may open a new way to the realization of ultra-narrow bandwidth filters.