Odd-even Effect on Liquid Crystalline Behavior for C_3-Cyclotriveratrylene(CTV) Derivatives Containing Alkoxies with Different Lengths as Peripheral Groups

A series of bowlic cyclotriveratrylenes（CTV） with peripheral groups with different lengths were synthesized.These compounds were investigated by diferential scanning calorimetry and hot stage coupled polarizing microscopy.Several CTV derivatives show thermotropic liquid crystalline properties.The experimental results of their thermotropic liquid crystalline behavior indicate that the clear points,the entropy changes of melting points,the crystallization temperatures,and their entropy changes all exhibited an evident odd-even effect except the melting points,which decreased monotonously with the increase of the length of the alkoxy groups.The parameter values of CTVs with even number carbon atoms were larger than those of CTVs with odd number.When the length of alkoxyl chains was even longer,a monotonous decrease occured.Nevertheless,in the case of the entropy changes of both melting points and crystallization temperatures,the effect was valid for all the six species,and therefore,the whole curves presented as a zig-zag form.

ODD-EVEN EFFECT OF LYOTROPIC LIQUID CRYSTALLINE PROPERTIES OF AROMATIC-ALIPHATIC COPOLYAMIDES

A series of aromatic-aliphatic copolyamides containing different aliphatic diamine units was synthesized by low temperature solution polycondensation.The liquid crystalline critical concentration(c^(*))and liquid crystalline critical temperature(T^(*))of these copolyamides exhibited an odd-even zigzag effect with the odd-even variation of carbon atom number in the aliphatic diamines used.

Anion Photoelectron Spectroscopy and Density Functional Theory Studies of AuC_(n)^(-/0)(n=3-8):Odd-Even Alternation in Electron Binding Energies and Structures

We measured the photoelectron spectra of AuC_(n)^(-)(n=3-8)and conducted theoretical study on the structures and properties of AuC_(n)^(-/0)(n=3-8).It is found that the photoelectron spectra of AuC_(n)^(-)exhibit odd-even alternation.The spectral features of AuC_(3)^(-),AuC_(5)^(-),and AuC_(7)^(-)are much broader than those of AuC_(4)^(-),AuC_(6)^(-),and AuC_(5)^(-).The vertical detachment energies of AuC_(3)^(-),AuC_(5)^(-),and AuC_(7)^(-)are lower than those of AuC_(4)^(-),AuC_(6)^(-),and AuCs_(8)^(-).The most stable structures of AuC_(n)^(-)(n=3-8)are chain structures.The most stable structures of neutral AuC_(n)(n=3-8)are linear structures except that those of AuC_(3) and AuC_(5) are slightly bent.The calculated∠AuCC angles,Au-C bond lengths,and the charges on Au atom also show odd-even alternations,consistent with the experimental observations.

A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Moments of Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments ofinertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC)method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNCcalculations show that the large odd-even difference in moments of inertia mainly comes from theinterference contributions j(μv) from particles in high j intruder orbitals μ and v quite near theFermi surface, which have no counterpart in the BCS formalism. The effective monopole andquadrupole pairing interaction strengths are determined to fit the experimental odd-even differencesin binding energies and bandhead moments of inertia. The experimental results for the variation ofmoments of inertia with rotational frequency ω are reproduced well by the PNC calculation. Thenearly identical experimental moments of inertia between ~(236)U(gsb) and ~(238)U(gsb) at lowfrequencies hω ≤ 0.20 MeV are also reproduced quite well.

（N-Z） Odd-Even Effect for the Non-Equilibrium Mechanism of （p, n） Reactions

The neutron spectra and angular distributions from （p,n） reactions in the input proton energy range 6-25 MeV were analyzed. These are the old experimental data, however, re-analysis of these data reveals very interesting peculiarities which never have been discussed before. The high energetic part of neutron spectrum due to the direct mechanism changes considerably from one isotope to other. This difference was described with incorporation of two components which provide the ＂broad bump＂, or ＂step like＂ shape of neutron spectra at high energy. The properties of these components are： different shape, energy shift between them, and very strong fluctuation between different isotopes for ratio of cross sections connected with partial contribution. One may conclude that shape of non-compound neutron spectrum demonstrates very strong （N-Z） odd-even effect. The direct comparison of experimental data, and semi-empirical results with （p,n） spectra predicted by the EMPIRE code, gave evidence that the traditional approach cannot predict this effect. New finding may explain the ＂constant temperature＂ dependence for level density in mass range A-60 discussed in several investigations. These new experimental peculiarities were demonstrated, and it may be considered as reality. At the same time there is not consequent physical model for their explanation. The fact that spectrum shape is correlated with N-Z value may give a hint that discussed effects are connected with ＂halo-neutrons＂.

DFT Study of Charge Effect on the Odd-even Oscillatory Behavior in Stabilities for Gold Clusters

The comparative study of charge effect on the size-dependence stabilities of gold clusters Aun^z （n = 2-12, z = 0/±1） in gas phase is performed at the M06-L/Lanl2dz level. The lowest-energy structures charged by -1, 0 and ＋1 are optimized. The result shows that the geo- metries of the clusters with over 7 atoms tend to be cake-like. From the two- to three-dimensional geometries, the oscillatory behaviors are exhibited in the structural and electronic properties with the most pronounced in energy gap. The amplitude for the positive clusters is bigger than both the neutral and negative clusters. The neutral clusters with even number of even-coordinated atoms are more stable than the neighbors with odd number of even-coordinated atoms, as is completely reversed for the charged clusters. The oscillatory behaviors for the charged clusters are opposite to that for the neutral clusters, as is attributed to the electron-paired effect.

First-Principles Study on Switching Performance and Spin Filtering Efficiency of Dimethyldihydropyrene/Cyclophanediene Single-Molecule Devices with Zigzag Graphene Nanoribbon Electrodes

Moleculardeviceswith highswitchingperformance and/or the perfect spin filtering effect have always been the pursuit with the development of molecular electronics.Hereb,yusingthe 2001.0V nonequilibrium.Green's function method in combination with the density functionaltheory,the switching performance and spin filtering properties of dimethyldihydropyrene(DHP)/cyclophanediene(CPD)photoswitchable molecule connected by carbon atomic chains(CACs)to two zigzag graphene nanoribbon electrodes have been theoretically investigated.The results show that DHP is more conductive than CPD and therefore an evident switching effect is demonstrated,and the switching ratio(RON/OFF)can reach 4.5×103.It is further revealed that the RoON/OF of DHP/CPD closely depends on the length of CACs.More specifically,the RoN/OFF values of DHP/CPD with odd-numbered CACs are larger than those with even-numbered CACs.More interestingly,a high or even perfect spin filtering effect can be obtained in these investigated DHP/CPD single-molecule devices.Our study is helpful for future design of single-molecule switches and spin filters and provides a way to optimize their performance by means of varying the length of bridging CACs.

秦九韶“大衍总数术”中问数化定数算法解析

秦九韶在"大衍总数术"中化问数为定数有两条途径:一是将诸问数直接两两连环求等;一是将诸问数先求总等,存一(位)约众(位),然后再连环求等。连环求等时的根本原则是"约奇弗约偶",其中的"奇"、"偶"系指等数的个数的单、双。"约奇弗约偶"就是在化约时约含有奇数个等数的问数而不约含有偶数个等数的问数,目的是使约后的两数互素。如果化约后得到的两数不互素,即属有续等的情形,此时要用"以续等约彼则必复乘此"的方法再次化约。若约后仍有续等,则要继续用此方法化约,直至求得定数。诸问数的排列顺序以及求等化约的先后次序不会影响计算结果的正确性。两种求定数的途径异曲同工,秦氏的算法是具有一般性的通法。

Probing the structure of multi-center molecules with odd–even high harmonics

We study high-order harmonic generation(HHG)from multi-center asymmetric linear molecules numerically and analytically.Our simulations show that odd and even HHG spectra of the asymmetric multi-center system respond differently to the change of the molecular structure.Specifically,when the internuclear distances between these nuclei of the molecule have a small change,the odd spectra usually do not change basically,but the even spectra differ remarkably.Based on this phenomenon,a simple procedure is proposed to probe the positions of these nuclei with odd–even HHG.Our results shed light on attosecond probing of the structure of multi-center molecules using HHG.

Forms of Rare Earth Elements in Soils: Ⅱ. Differentiation of Rare Earth Elements

The present paper deals mainly with the relationships between the distribution of rare earth elements (REE) in different forms in soils and the atomic number and with the odd-even phenomenon in the distribution of ionic lanthanides in soils.The enrichment tendency of light REE relative to heavy REE in soils was pointed out on the experimental results about the proportions of Ce-group and Y-group elements in different REE forms in soils.Meanwhile,the differentiation of Tm in different soil REE forms was compared and the reasons why Tm is enriched in soils were preliminarily discussed.

Design and Simulation of Routing-switching Protocol Based on Optical Switch Array

An optical routing-switching technology based on optical switch array is proposed.The characteristics of the blocking and nonblocking networks are analyzed and compared,odd-even sorting network is used to realize optical routing-switching,relative routing-switching protocol is designed.Simulation test under load shows that it can reduce a blocking effectively and enhance an efficiency of switching.Further,it can transfer the processing and switching within parallel computer from electric domain to optical domain. It can make parallel computer coordinating computing and processing at much more higher speed, storing and transmitting even more efficiently.

Studies on Liquid Crystalline Bis[4-(p-phenoxy)-phenylbenzoate]Alkyldicarboxylat

A new series of liquid crystals of bis[4-(p-phenoxy)-phenylbenzoate]-alkyldicarboxylate which contain two rigid groups connected by a flexible spacer was synthesized. These liquid crystals show nematic phase and were found to show odd even effect in isotropization temperature and entropy change.

Density-controlled Delaunay triangulation for 2D sea area

Triangulation is widely used in scientific research, such as finite element mesh generation, surface reconstruction and the reconstruction of the density field data. This paper proposes a new method combining image processing and density-controlled Centroidal Voronoi tessellations to quickly generate a density-controlled constrained Delaunay triangulation lbr 2D sea area. Firstly, preprocess digital images of the sea area and extract the boundary of seawater region by eight-neighbor searching algorithm. Then, 1 use Odd-Even Testing＂ method to check if one random vertex is inside the boundary and insert random vertices into the boundary. Finally, we get the CDT of random vertices by density-controlled CVT-Lloyd method. We also give some comparisons with existing methods, and our method performs better in final restllt of triangulation.

Generalized Odd-Even Mode Theory and Mode Synthesis Antenna Design Approach

In this article,studies on the multimode excitation problem of waveguides and antennas,the balance/unbalance mech-anism and the balanced feeding techniques in dipole antenna systems are first briefly historically reviewed.In this context,general-ized odd-even mode theory is advanced to quantitatively and approximately describe the mutual coupling effect between a feed line and an antenna.As is mathematically deduced and demonstrated,the modal parity mismatch between the feed line and the antenna should ultimately dominate the unbalance phenomenon in antenna systems.Thus,an elegant,closed-form formula is derived to ap-proximately calculate the“unbalance degree”of a straight dipole off-center fed by a symmetric twin-wire line.Design approaches for the simplest,linear,1-D multimode resonant antennas are introduced.Moreover,the“falling tone excitation”law gauged based on prototype dipoles is revealed and used to develop a mode synthesis design approach for microstrip patch antennas(MPAs)and 2-D sectorial electric dipole antennas.Design examples with distinctive radiation performance are presented and discussed.Finally,possible development trends of multimode resonant antennas are prospected.

Abnormal odd-even staggering behavior around^132Sn studied by density functional theory

In this work,we have performed Skyrme density functional theory(DFT)calculations of nuclei around^132Sn to study whether the abnormal odd-even staggering(OES)behavior of binding energies around N=82 can be reproduced.With the Skyrme forces SLy4 and SkM*,we tested the volume-and surface-type pairing forces and also the intermediate between these two pairing forces,in the Hartree-Fock-Bogoliubov(HFB)approximation with or without the Lipkin-Nogami(LN)approximation or particle number projection after the convergence of HFBLN(PLN).The Universal Nuclear Energy Density Function(UNEDF)parameter sets are also used.The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force.Moreover,for the pairing force that is favored more at the nuclear surface,a larger mass OES is obtained,and vice versa.It appears that the combination of volume and surface pairing can give better agreement with the data.In the studies of the OES,a larger ratio of surface to volume pairing might be favored.Additionally,in most cases,the OES given by the HFBLN approximation agrees more closely with the experimental data.We found that both the Skyrme and pairing forces can influence the OES behavior.The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one.The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around^132Sn.The neutron OES of the tin isotopes given by the SkM*force agrees more closely with the experimental one than that given by the SLy4 force in most cases.Both SLy4 and SkM*DFT have difficulties in reproducing the abnormal OES around^132Sn.Using the PLN method,the systematics of OES are improved for several combinations of Skyrme and pairing forces.

Odd-even staggering for production cross sections of nuclei near the neutron drip-line

In our previous studies[Phys.Rev.C 97,044619(2018);Phys.Rev.C 103,044610(2021)],a universal odd-even staggering(OES)has been observed in extensive cross sections of isotopes not far from stability,measured for different fragmentation and spallation reactions.Four OES relations have been proposed on the basis of this OES universality.However,it is still unclear whether this OES universality and OES relations are applicable to many isotopes near the drip-lines.Here,the OES in recent experimental cross sections of very neutron-rich nuclei approaching the drip-line(from ^(76)Ge,^(82)Se+^(9)Be)is quantitatively investigated,to further validate the OES universality and OES relations.The OES magnitudes in these experimental data approaching the neutron drip-line generally agree with those evaluated previously,mainly from experimental data near stability.New OES evaluations de-rived from these experimental data are also recommended for more exotic nuclei near the neutron drip-line,which extends the conclusions of our previous OES studies.In addition,the OES relation calculations are consistent with these experimental data of very neutron-rich nuclides according to their comparisons in this work.Finally,comparisons with additional experimental data(from ^(238)U+^(9)Be)also support that new OES evaluations and OES relation calculations can be applied for exotic nuclei near the neutron drip-line.

Systematic odd-even differences in the moments of inertia of superdeformed bands and blocking effect

A comprehensive analysis of the superdeformed bands observed near A≈190 indicates that there exist systematic odd-even differences in the moments of inertia similar to that observed in normally deformed nuclei, which can be considered as compelling evidence for pairing and blocking effect in super-deformed nudei. With increasing rotational frequency the odd-even differences become weaker and weaker due to the Coriolis anti-pairing effects. Particularly, the odd-even differences in the dynamic moments of inertia become obscure when hω≥2 MeV, and in certain cases there emerges nearly identical value of J(2) for some neighboring nudei. However, the odd-even differences in the kinematic moments of inertia still remain to certain extent at the highest frequencies.

Special Odd-Even Effect of Degree of Oligomerization on Properties of Cyclic Oligoesters

We demonstrate here seven pure cyclic samples, which belongs to two series of oligoesters, cyclic oligo（trimethylene terephthalate）s （COTTs） and cyclic oligo（butylene terephthalate）s （COBTs）, showing odd-even effect of degree of oligomerization （repeating units number） on properties. The pentamer of COTT and trimer of COBT show much lower melting temperature, and the trimer of COTT and trimer of COBT show significant lower refractive index, which can be ascribed to the low packing density of cyclic oligoesters with odd number of degree of oligomerization. Our results reveal the discrete property change as a function of cyclic size of oligomers, which can be used to design materials with special properties.

Odd-Even Sequence Effect of Surface-Mediated Peptide Assemblies Observed by Scanning Tunneling Microscopy

The peptide assembly structures of polyglutamine （PolyQ） have been studied by using scanning tunneling microscopy （STM） with high spatial resolution in ambient conditions. 4,4＇-Bipyridyl （4Bpy） was introduced into the PolyQ7 and PolyQ8 peptide assemblies for labeling the C-termini of the peptides. The fine structures of the 4Bpy-PolyQ7 and 4Bpy-PolyQ8 co-assemblies are observed, and the statistics of the apparent peptide strand length reveal different length distributions for PolyQ7 and PolyQs. One predominant apparent peptide strand length is ob- served for PolyQ7 reflecting one predominant peptide conformation in assembly structures, while three major ap- parent strand lengths can be identified with PolyQ8 reflecting three co-existing peptide conformations in peptide as- semblies. Such drastic difference in assembling characteristics can be considered as a reflection of asymmetric ad- sorption effect ofpeptides relating to odd-even residue numbers of PolyQ7 and PolyQ8,