A study of Feynman integrals by micro-differential equations

We use the holonomic character of Feynman integrals to describe their singularity structure explicitly in some simple cases. The results in §1 show that under moderate conditions Feynman amplitudes can be locally expressed essentially in terms of Legendre functions near the points where two positive- Landau-Nakanishi surfaces meet. Related topics such as hierarchical principle in perturbation theory are also discussed in terms of holonomic systems involved. In §4 we use the concrete expressions for Feynman amplitudes obtained in §1 to discuss the validity of Sato's conjecture.Supported in part by NSF MCS 75-2333Supported in part by NSF GP 36269     

A novel synthesis of amino acid derivatives of phospholene oxides

A convenient synthetic approach is established to prepare a new class of 1-l-α-amino acid derivatives of phospholene oxides by amination of (±)-1-chloro-2-phospholene-1-oxides with several optically pure l-α-amino acid esters. All compounds obtained as a diastereomeric mixture in good to high yields. The two diastereomers were successfully separated by column chromatography and structurally identified by their spectral analyses.     

Photoreactive polyamides having m- or 1-type dimer moiety derived from 4-(3-oxo-3-phenyl-1-propenyl)benzoic acid derivatives

Photoreactive polyamides having m- or 1 -type cyclobutane moiety were prepared via a topochemical photodimerization of 4-(3-oxo-3-phenyl-1-propenyl)benzoic derivatives,⁴ followed by polycondensation of cyclobutane dicarboxylate derivatives with diamines. From the spectral studies of resulted polyamides compared with the corresponding reference diamides, it was concluded that both types of polyamides were depolymerized photochemically to give the same type of amide derivative having chalcone moiety with a small amount of undefined side reaction. The cyclobutane ring of the m-dimer from 4-(3-oxo-3-phenyl-1-propenyl)benzoic acid in crystal is severely twisted presumably because of the enhanced steric repulsions between two pairs of adjacent substituents. The higher quantum yield of the m-dimer for the photocleavege, compared with that of the 1 -dimer, has been interpreted in terms of such steric repulsions by the strained structure of the m-dimer.     

Cover Picture

The cover picture shows a section of the electron charge density of the first metal carbide endohedral metallofullerene (Sc(2)C(2))@C(84) obtained from a synchrotron X-ray powder diffraction study by the maximum entropy method (MEM). The several density maxima, which correspond to scandium and carbon atoms, are clearly seen inside the C(84) carbon cage. The MEM charge density distribution also reveals that the C(84) cage has D(2d) symmetry (no. 23) and that the C(2) axis is parallel to the <100> face-centered cubic (fcc) direction of the unit cell. As a consequence of the site symmetry being 4mm, the C(2) axis of (Sc(2)C(2))@C(84) is oriented to six equivalent <100> directions and shows a merohedral disorder. The resultant Sc small middle dot small middle dot small middle dotSc distances and C-C bond lengths of the Sc(2)C(2) cluster are 0.429(2) and 0.142(6) nm, respectively. The observed C-C bond length is between that of a typical single and a double bond, and is very close to that of the C-C bond (0.143 nm) combining two pentagons in a C(60) molecule. More about this fascinating structure can be found in the contribution by Shinohara and co-workers on p. 397 ff.     

Manipulating the Through‐Space Spin–Spin Interaction of Organic Radicals in the Confined Cavity of a Self‐Assembled Cage

We show a new approach to manipulating the through‐space spin–spin interaction by utilizing the confined cavity of a self‐assembled M₆L₄ coordination cage. The coordination cage readily encapsulates stable organic radicals in solution, which brings the spin centers of the radicals closer to each other. In sharp contrast to the fact that the radical in solution in the absence of the cage is in a doublet state, in the presence of the cage through‐space spin–spin interaction is induced through cage‐encapsulation effects in solution as well as in the solid state, resulting in the triplet state of the complex. These results were confirmed by ESR spectroscopy and X‐ray crystallography. The quantity of triplet species generated by encapsulation in the cage increases with increasing affinity of the radicals to the cage. We estimated the affinity between several types of guests and the cage in solution by cyclic voltammetry. We also demonstrate that the through‐space interaction of organic radicals within the self‐assembled coordination cage can be controlled by external stimuli such as heat or pH.     

Diastereoselective imino-aldol condensation of chiral 3-(p-Tolylsulfinyl)-2-furaldimine and ester enolates

(Ss)-3-(p-Tolylsufinyl)-2-furaldimine was synthesized, and condensation of the chiral furaldimine with lithium ester enolates has been examined. The product distribution of the reaction is dependent upon reaction conditions and on the kind of the substituent placed on the esters. Disubstituted ester enolate resulted in the exclusive formation of (4R)-beta-lactam, while unsubstituted, tert-butyl ester enolate preferentially gave (3R)-beta-amino ester. With the monosubstituted ester enolates, the condensation afforded (4R)-beta-lactams and/or (3R)-beta-amino esters as major products. This method has been applied to an efficient route to chiral furyl beta-lactams.     

Investigation of the crystal structure and the structural and magnetic properties of SrCu2(PO4)2

SrCu2(PO4)2 was prepared by the solid-state method at 1153 K. Its structure was solved by direct methods in the space group Pccn (No. 56) with Z = 8 from synchrotron X-ray powder diffraction data measured at room temperature. Structure parameters were then refined by the Rietveld method to obtain the lattice parameters, a = 7.94217(8) A, b = 15.36918(14) A, and c = 10.37036(10) A. SrCu2(PO4)2 presents a new structure type and is built up from Sr2O16 and Cu1Cu2O8 units with Cu1...Cu2 = 3.256 A. The magnetic properties of SrCu2(PO4)2 were investigated by magnetic susceptibility, magnetization up to 65 T, Cu nuclear quadrupole resonance (NQR), electron-spin resonance, and specific heat measurements. With spin-dimer analysis, it was shown that the two strongest spin-exchange interactions between Cu sites result from the Cu1-O...O-Cu2 and Cu2-O...O-Cu2 super-superexchange paths with Cu1...Cu2 = 5.861 A and Cu2...Cu2 = 5.251 A, and the superexchange associated with the structural dimer Cu1Cu2O8 is negligible. The magnetic susceptibility data were analyzed in terms of a linear four-spin cluster model, Cu1-Cu2-Cu2-Cu1 with -2J(1)/kB = 82.4 K for Cu1-Cu2 and -2J(2)/k(B) = 59 K for Cu2-Cu2. A spin gap deduced from this model (Delta/kB = 63 K) is in agreement with that obtained from the Cu NQR data (Delta/kB = 65 K). A one-half magnetization plateau was observed between approximately 50 and 63 T at 1.3 K. Specific heat data show that SrCu2(PO4)2 does not undergo a long-range magnetic ordering down to 0.45 K. SrCu2(PO4)2 melts incongruently at 1189 K. We also report its vibrational properties studied with Raman spectroscopy.     

Facile Synthesis and Palladium‐Catalyzed Cross‐Coupling Reactions of 2,3‐Bis(pinacolatoboryl)‐1,3‐butadiene

Treatment of 1,1‐bis(pinacolatoboryl)ethene with an excess of 1‐bromo‐1‐lithioethene gave 2,3‐bis(pinacolatoboryl)‐1,3‐butadiene in high yield. Palladium‐catalyzed cross‐coupling of the resulting diborylbutadiene with aryl iodides took place smoothly in the presence of a catalytic amount of Pd(OAc)₂/PPh₃ and aqueous KOH to give 2,3‐diaryl‐1,3‐butadienes in good yields. The coupling reaction with commercially available 4‐acetoxyphenylmethyl chloride under the same conditions followed by hydrolysis of the acetyl groups gave anolignan B in a one‐pot manner. A variety of [3]‐ to [6]dendralenes were synthesized by palladium‐catalyzed coupling of the diene or 1,1‐bis(pinacolato)borylethene with alkenyl or dienyl halides, respectively, in good yields.     

Quantum Stream Cipher Based on Holevo–Yuen Theory

In this review paper, we first introduce the basic concept of quantum computer-resistant cryptography, which is the cornerstone of security technology for the network of a new era. Then, we will describe the positioning of mathematical cryptography and quantum cryptography, that are currently being researched and developed. Quantum cryptography includes QKD and quantum stream cipher, but we point out that the latter is expected as the core technology of next-generation communication systems. Various ideas have been proposed for QKD quantum cryptography, but most of them use a single-photon or similar signal. Then, although such technologies are applicable to special situations, these methods still have several difficulties to provide functions that surpass conventional technologies for social systems in the real environment. Thus, the quantum stream cipher has come to be expected as one promising countermeasure, which artificially creates quantum properties using special modulation techniques based on the macroscopic coherent state. In addition, it has the possibility to provide superior security performance than one-time pad cipher. Finally, we introduce detailed research activity aimed at putting the quantum stream cipher into practical use in social network technology.     

Diagonal reflection symmetries and universal four-zero texture

In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_u,v^*,R=m_u,v,m_d,e^*=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα_2.3/2-0π/2.Realization of diagonal reflection symmetries implies a broken chiral U(1)po symmetry only for the first generation.The axion scale is suggested to be(θ_u,d)~△GuT√m_{u,dm_(c,s})/v-10¹²[GeV].By combining the symmetries with the four-zero texture,the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well.This scheme predicts the normal hierarchy,the Dirac phase ocp≈203°,and|ml|≈2.5 or 6.2[meV].In this scheme,the type-I seesaw mechanism and a given neutrino Yukawa matrix Y_ycompletely determine the structure of the right-handed neutrino mass M_R.A u-y unification predicts the mass eigenvalues to be(M_RI,M_R2,M_R3)=(O(10⁵).O(10⁹),O(10¹⁴)[Gev].