Short—Time Critical Behavior Affected by Weakly Long—Range Interactions

The theoretic renormalization group approach is applied to the study of short-time critical behavior of the Ginzburg–Landau model with weakly long-range interactions . The system initially at a high temperature is firstly quenched to the critical temperature and then released to an evolution with a model A dynamics. A double expansion in and with of order is employed, where is the spatial dimension. The asymptotic scaling laws and the initial slip exponents and for the order parameter and the response function respectively are calculated to the second order in for close to 2.

A 3-D Hybrid Framework {[(dafone)PbI_2](dafone)_2}_n Constructed from Weak Interactions by Introducing Aromatic H-bond Acceptors: Synthesis and Theoretical Study

A new 3-D hybrid framework {[（dafone）PbI2]（dafone）2}n 1 （dafone = 4,5-diazafluoren-9-one） has been prepared and structurally determined. 1 crystallizes in the monoclinic system, space group C2/c with a = 24.109（8）, b = 16.596（8）, c = 7.983（3）A, β = 91.590（15）°, V = 3193（2）A^3, Z = 4, C33H18I2N6O3Pb, Mr = 1007.53, Dc = 2.096 g/cm^3, F（000） = 1880, μ（MoKα） = 7.262 mm^-1, the final R = 0.0352 and wR = 0.0951 for 3198 observed reflections with I 〉 2σ（I）. In the [（dafone）PbI2]n chain, the Pb center adopts a distorted octahedral coordination geometry and shares an edge to give a one-dimensional polymer. The 3-D arrangement of 1 constructs from H-bonds among dafone molecules and π-π stacking interactions among dissociative dafone molecules. These weak interactions contribute to the stability of the title compound. DFT calculation was carried out to reveal its electronic structure.

Interesting Weak Interactions in Three Silver Coordination Polymers Based on Tetrafluorobenzenedicarboxylate and Benzonitrile Ligands

The assembly reactions of o- （or m-, or p-） tetrafluorobenzenedicarboxylic acid （denoted as o-H2L, m-H2L and p-HzL, respectively）, benzonitrile and Ag＋ ion led to three compounds： [Ag2（PhCN）2（o-HL）2]n （1）, [Ag2（PhCN）2（m-HL）2]n （2） and [Ag2（PhCN）2（p-L）], （3）. 1 and 2 feature a 1D coordination chain, while 3 bears a 2D net structure. A variety of weak interactions are observed in the compounds. Strong nwrinteractions connect the 1D chains into a 3D supramolecular network in 1. Hydrogen bonds connect the chains into layers in 2. Three types of interesting π-π interactions also assemble the 2D layers into a 3D overall structure in 3.

The Weak Interaction on CO_2...CO van der Waals Complex: A Theoretical Study

The geometries of van der Waals complex CO 2...CO were optimized at DFT and second order Moller Plesset perturbation(MP2) levels with the large basis set, three stable structures were found. The most stable structure has a T shape geometry in which the CO lies along the C 2 axis of CO 2, with the two C atoms direct contact and R (C...C)=0 3227 nm. The corresponding energies of the most stable structure were calculated by means of MP2, MP4D, MP4DQ, MP4SDTQ, MP4SDQ, CCSD and CCSD(T) methods. The BSSE(basis set superposition error) was eliminated by the Boys Bernardi counterpoise correction(CP) method. According to thermodynamics data, van der Waals complex CO 2...CO can be found at a low temperature and/or a high pressure. There is a little charge transferred between the two interacted subunits. In the most stable structure, CO 2 is the acceptor and CO is the donor.

Three Clifford Algebras for Four Kinds of Interactions

Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the electron. The Clifford algebra of space-time is enough for electro-weak interactions. To get the gauge group of the standard model, with electro-weak and strong interactions, a third algebra is sufficient, with only two more dimensions of space. The Clifford algebra of space allows us to include also gravitation. We discuss the advantages of our approach.

One-dimensional Chain Topology in [Ag(C_6H_6NCl)_2](ClO_4), Generated through Weak Interaction between Molecules

The mononuclear complex [Ag(C6H6NCl)2](ClO() has been prepared and structurally analyzed by single-crystal X-ray diffraction. The complex crystallizes in the monoclinic system, space group C2/c with unit cell parameters: a=15.5314(2), b=8.0247(8), c=15.3701(2)?.β=118.832(2)°, V=1678.2(3)?3, Z=4, Mr=462.46, Dc=1.830Mg/m3, F(000)=912, μ(MoKα) = 1.694cm-1. The final R and wR are 0.0472 and 0.1272 for 1484 observed reflections with I≥3σ(I). The Ag atom is coordinated by two nitrogen atoms of 4-chloromethyl-pyridine in a linear coordination geometry. Each molecule is further linked by the weak interaction between the Cl and Ag atoms to form a one-dimensional chain structure with Ag－Cl distance of 3.240?.

Crystal Structure and Interaction with DNA of [Ni(phen)(mal)(H_2O)_2]·3H_2O

A new complex [Ni（phen）（mal）（H2O）2]·3H2O （phen = 1,10-phenanthroline, real^2- = malonic acid） has been synthesized by the reaction of nickel nitrate, phen and malonic acid. EA, IR spectra and X-ray single-crystal diffraction were carried out to determine the composition and crystal structure of the title complex. Crystal data： monoclinic system, space group P2/c,α = 8.937（3）, b = 12.163（5）, c = 9.725（3） A,β = 119.36°, C15H19N2O9Ni,Mr= 430.03, Z = 2, F（000） = 446, V= 921.3 A3, Dc = 1.550 g/cm^3, μ= 1.104 mm^-1, -10≤h≤10, -12≤k≤ 14, -11≤1≤7, R = 0.0261 and wR = 0.0609 for 4376 （Rint = 0.0203） independent reflections and 1631 observed ones （I 〉 2σ（I））. Ni（Ⅱ） exhibits an octahedral coordination geometry, with hydrogen bonds and π-π interactions stabilizing the whole structure. UV spectrum of the complex interacting with protamine DNA indicates that the title compound interacts with DNA via insertion mode with bonding constant Kb of 1. 11 × 10^4.

Weak Interactions and 2D Layer Structure of a New Ion-pair Complex Bis(1-benzyl-4-methylquinolinium)-bis(maleonitriledithiolato)nickel(Ⅱ)

A new ion-pair complex, [BzMeQ1]2[Ni（nmt）2]1（[BzMeQ1]^＋ = 1-benzyl-4-ntethylquino- linium, mnta- -- maleonitriledithiolate） has been synthesized and structurally characterized by IR, ESI-MS and X-ray diffraction methods. Complex 1 is of triclinic, space group PI, with a = 9.079（2）, b = 10.154（2）, c = 11.243（2）A, α= 81.58（1）, β= 69.63（1）, γ = 68.02（1）°, V= 940.1（3）A3, Dc = 1.427 g/cm^3, Z = 1, F（000） = 418 and R = 0.0442. A 2D layer structure is formed via the cation-cation π…π and C-H…π interactions observed in the solid state of the complex.

NMR STUDIES ON THE WEAK INTERACTION OF FOUR-MONONUCLEOTIDES WITH TRYPTAMIDE AND LEUCINAMIDE

NMR spectroscopy analysis was introduced to investigate the weak interaction of four 5'—mononucleotides with tryptamide and leucinamide. Assuming a 1∶1 complex formation, the association constants were determined by nonlinear regression analysis. The association affinity of 4 mononucleotides with tryptamide decreased in the order: G>A>C>U, indicating that purine bases stack more strongly with tryptamide than pyrimidine bases. But with leucinamide the affinity decreases in the order: G>C>A=U, suggesting an amino acid—anticodonic preferential interaction. The implication of the present data to the origin of genetic code was briefly discussed.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

Towards the Unification of All Interactions (The First Part: The Spinor Wave)

For the unification of gravitation with electromagnetism, weak and strong interactions, we use a unique and very simple framework, the Clifford algebra of space . We enlarge our previous wave equation to the general case, including all leptons, quarks and antiparticles of the first generation. The wave equation is a generalization of the Dirac equation with a compulsory non-linear mass term. This equation is form invariant under the group of the invertible elements in the space algebra. The form invariance is fully compatible with the gauge invariance of the standard model. The wave equations of the different particles come by Lagrange equations from a Lagrangian density and this Lagrangian density is the sum of the real parts of the wave equations. Both form invariance and gauge invariance are exact symmetries, not only partial or broken symmetries. Inertia is already present in the part of the gauge group and the inertial chiral potential vector simplifies weak interactions. Relativistic quantum physics is then a naturally yet unified theory, including all interactions.

Selection Rules in Weak Interaction and Conservation of Fermion Quantum Number

Traditionally, in weak interaction, I3, Y and four flavour quantum numbers are not conserved but several empirical selection rules work well. Recently, it was found that, in weak interaction, there are three levels of conservation of additive quantum numbers, and fermion quantum number F is conserved in all kinds of interactions. It is known that weak interaction has three types: fermionic, pure hadronic and pure leptonic, corresponding to the first and the second level of conservation of additive quantum numbers respectively. It is demonstrated in this paper that the selection rules in all types of weak interaction can be interpreted by conservation of F, and the formula of relation between Q/e, F and F0 is more general than Gell-Mann-Nishijima formula. Description of weak interaction becomes simpler, If only we take Q, F0 and F, based on the conserved physical quantities.

The Origin, Properties and Detection of Dark Matter and Dark Energy

The pictures from the James Webb Space Telescope (JWST) suggest that massive galaxies were already at the beginning of the expansion of the Universe because there was too short time to create them. It is consistent with the new cosmology presented within the Scale-Symmetric Theory (SST). The phase transitions of the initial inflation field described in SST lead to the Protoworld—its core was built of dark matter (DM). We show that the DAMA/LIBRA annual-modulation amplitude forced by the change of the Earth’s velocity (i.e. baryonic-matter (BM) velocity) in relation to the spinning DM field in our Galaxy’s halo should be very low. We calculated that in the DM-BM weak interactions are created single and entangled spacetime condensates with a lowest mass/energy of 0.807 keV—as the Higgs boson they can decay to two photons, so we can indirectly detect DM. Our results are consistent with the averaged DAMA/LIBRA/COSINE-100 curve describing the dependence of the event rate on the photon energy in single-hit events. We calculated the mean dark-matter-halo (DMH) mass around quasars, we also described the origin of the plateaux in the rotation curves for the massive spiral galaxies, the role of DM-loops in magnetars, the origin of CMB, the AGN-jet and galactic-halo production, and properties of dark energy (DE).

Calculation of the Standard Model Parameters and Particles Based on a SU(4) Preon Model

This paper describes an extension and a new foundation of the Standard Model of particle physics based on a SU(4)-force called hyper-color, and on preon subparticles. The hyper-color force is a generalization of the SU(2)-based weak interaction and the SU(1)-based right-chiral self-interaction, in which the W-and the Z-bosons are Yukawa residual-field-carriers of the hyper-color force, in the same sense as the pions are the residual-field-carriers of the color SU(3) interaction. Using the method of numerical minimization of the SU(4)-action based on this model, the masses and the inner structure of leptons, quarks and weak bosons are calculated: the mass results are very close to the experimental values. We calculate also precisely the value of the Cabibbo angle, so the mixing matrices of the Standard model, CKM matrix for quarks and PMNS matrix for neutrinos can also be calculated. In total, we reduce the 29 parameters of the Standard Model to a total of 7 parameters.

Synthesis and Crystal Structure of a Two-dimensional Framework Supramolecular Complex [Mn(phen)(DPZDA)(H_2O)]·2H_2O

A novel two-dimensional supramolecular complex [Mn（phen）（DPZDA）（H2O）]·2H2O has been synthesized by the reaction of Mn（CH3COO）2, 1,10-phenanthroline （phen） and H2DPZDA （3,5-dimethyl-pyrazine-2,6-dicarboxylic acid）. Elemental analysis, IR spectra and X-ray singlecrystal diffraction were carried out to determine the composition and crystal structure of the title complex. Crystal data： triclinic system, space group P1, a = 7.7474（13）, b = 9.3381（15）, c = 15.146（3） A, α = 93.872（3）, β= 102.451 （11 ）, y = 105.261 （ 11）°, C20H20MnN4O7, Mr = 483.34, Z = 2, F（000） = 498, V=1023.2（3）A^3, Dc=1.569 g/cm^3,μ=0.697 mm^-1, -9≤h≤9, -11≤k≤10, -18≤l≤12, R = 0.0365 and wR=0.0901 for 3585 independent reflections （Rint= 0.0165） and 2923 observed reflections （I〉 2σ（I））. Structural analysis indicates that Mn（Ⅱ） adopts a distorted octahedral geometry. The 2-D framework supramolecular structure of the title complex is constructed from hydrogen bonds and π…π interactions.

Crystal Structure and Theoretical Studies of Tetrahytrate(1-H-1,2,4-triazole-3,5-dicarboxylicacid)nickel

A new compound, [Ni（Hdctrz）（H2O）4]（1, H3dctrz = 1-H-1,2,4-triazole-3,5-dicarboxylic acid）, has been successfully synthesized via slow evaporation. The structure of 1 was characterized by FT-IR, elemental analysis and single-crystal X-ray diffraction. Compound 1 crystallizes in monoclinic, space group P21/c with a = 6.871（1）, b = 11.468（1）, c = 12.178（1） A, b = 101.291（1）o, V = 941.01（16） A3, Z = 4, C4H9N3O8Ni, Mr = 285.85, Dc = 2.018 g·cm–3, m = 2.10 mm–1, F（000） = 584, GOOF = 1.025, the final R = 0.0515 and wR = 0.2125 for 1404 observed reflections（I 〉 2s（I））. The crystal structure is assembled by a slightly distorted {NiNO5} octahedral geometry and hydrogen bonds viz. N–H…O, O–H…O, C–O…π and π···π weak interactions. A rare π···π interaction from triazolate and carboxylate is affirmed through the molecular orbitals（MO） of three adjacent Ni CN molecules. The 3D Hirshfeld surface analysis was employed to gain additional insight into the interactions responsible for the packing of compound 1. Quantitative examination of 2D fingerprint plots revealed, amongst others, the dominating participation of O···H, N···H and π···π interactions in the molecular packing.

Hydrothermal Synthesis and Structure Characterization of Compound Zn(Hpydc)_2(H_2O) (pydc=pyridine-2,5-dicarboxylate)

The hydrothermal reaction of ZnO, H3PO4(85%), (H2NCH2CH2)2NH and H2pydc results in the formation of a discrete mononuclear zinc(II) complex Zn(Hpydc)2(H2O). It crystallizes in monoclinic space group C2/c with a = 17.9947(8), b = 7.1875(3), c = 12.5895(4) , b = 110.802(2), V = 1522.14(10) 3, Z = 4, Mr = 415.61, (C14H10N2O9Zn), Dc = 1.814g/cm3, = 16.71cm-1, F(000) = 840, R = 0.0505, wR = 0.1144. Each zinc(II) is coordinated to two nitrogen and three oxygen atoms of which two nitrogen and two oxygen atoms are from two pydc ligands, and one oxygen atom from the coordinated water molecule to form an irregular polyhedral geometry. The complex is linked further into a three-dimensional structure through the weak interactions of hydrogen bonds between the two oxygen atoms. IR spectrum of the complex is also discussed.

Solvothermal Synthesis and Structure Characterization of a 3D Hydrogen-bonded Copper Compound [Cu(H_2dhpmc)_2]·2H_2O

The solvothermal reaction of H3dhpmc (H3dhpmc = 2, 4-dihydroxypyrimidine- 5-carboxylic acid), CuCl2稨2O and NaVO3 results in the formation of a discrete mononuclear Cu(Ⅱ) complex [Cu(H2dhpmc)2]?H2O. It crystallizes in monoclinic system, space group P21/c with a = 5.0497(9), b = 10.0196(6), c = 13.715(2) ? b = 96.237(1)? V = 689.8(2) 3, Z = 2, Dc = 1.973 g/cm3, ?= 1.654 mm-1, F(000) = 414, R = 0.0736 and wR = 0.1351. Each Cu(Ⅱ) is coordinated to four oxygen atoms of two 2, 4-dihydroxypyrimidine-5-carboxylic acid ligands in the equatorial position and two oxygen atoms of two water molecules in the axial position to form an axially elongated octahedral geometry. The title complex is further linked into a three-dimensional structure through the weak interactions of hydrogen bonds between the oxygen atoms and the nitrogen atoms.

Towards the Unification, Part 2: Simplified Equations, Covariant Derivative, Photons

We continue the study of the Standard Model of Quantum Physics in the Clifford algebra of space. We get simplified mass terms for the fermion part of the wave. We insert the simplified equations in the frame of General Relativity. We construct the electromagnetic field of the photon, alone boson without proper mass. We explain how the Pauli principle comes from the equivalence principle of General Relativity. We transpose in the frame of the algebra of space the second quantification of the electromagnetic field. We discuss the changes introduced here.

Synthesis, Characterization and Crystal Structure of a Dinuclear Silver(I) Complex: [AgL(NO_3)]_2 (L= 2-Acetamido-5-methyl-1,3,4-thiadiazole)

The title complex [AgL（NO3）]2 1, where L = 2-acetamido-5-methyl-1,3,4-thiadiazole, was prepared from the reaction of 2-acetamido-5-methyl-1,3,4-thiadiazole with AgNO3 at room temperature and its structure has been determined by single-crystal X-ray diffraction. The crystal is of monoclinic, space group P2t/c with a = 12.5454（8）, b = 11.9672（12）, c = 6.8925（6） A, β = 98.468（2）°. V= 1023.51（15） A^3, Mr= 3127.08, Dc = 2.123 g/cm^3, Z= 4, μ（MoKoσ） = 2.174 mm^-1, F（000） = 640, R = 0.0259 and wR = 0.0580 for 1787 observed reflections with I 〉 2σ（I）. Complex 1 self-assembls into a quasi-three-dimensional network consisting of adjacent dimers through intermolecular Ag...O weak interactions.