Do pentaurea calix[5]arenes form hydrogen bonded dimeric capsules?

Calix[5]arenes substituted at their wider rim by five urea residues do not form hydrogen bonded dimeric capsules in aprotic, apolar solvents, in contrast to their calix[4]arene analogs, although molecular dynamic simulations predict very similar geometrical parameters for both cases. The reason for this different behavior is most probably the higher energetic cost which must be paid to arrange the calix[5]arene skeleton in the C₅-symmetrical conformation required for the dimerization.     

Mass and decays of Brout-Englert-Higgs scalar with extra generations

The higher bound on the mass of the Brout-Englert-Higgs scalar boson arising from radiative corrections is not stable when the Standard Model is extended to include nondecoupling particles. In particular, additional generations of fermions allow for a heavier scalar. We investigate how the decay branchings of the scalar boson are affected by the opening of new channels. The text was submitted by the authors in English.     

Hunting for the alpha: <Emphasis Type="Italic">B</Emphasis> → ρρ, <Emphasis Type="Italic">B</Emphasis> → ππ, <Emphasis Type="Italic">B</Emphasis> → πρ

The hypothesis of the smallness of penguin contributions to charmless strangeless \(B_d (\bar B_d )\) decays allows one to determine with high accuracy the value of the angle α from the currently available B → ρρ, B → ππ, and B → πρ decay data.     

Phase locking in a multicore fiber laser by means of a Talbot resonator

We report phase locking of a diode-pumped multicore fiber laser with a circular array of 18 Nd-doped emitters (microcores) acting as an active medium. Phase locking was achieved in a Talbot resonator configuration. We present calculations of the effective reflection coefficients that are due to self-imaging. Far-field distributions and near-field pattern of several supermodes are calculated and compared with experimental results.     

Lectures on the theory of electroweak interactions

The theory of electroweak interactions is given in four lectures.     

Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices

In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor-train (QTT) structure. In particular, we show that the inverse of a complex circulant matrix $A$, generated by the first column of the form ${(a_0,\dots ,a_{m-1},0,\dots ,0,a_{-n},\dots ,a_{-1})}^{\top }$ admits a QTT representation with the QTT ranks bounded by $(m+n)$. Under certain assumptions on the entries of $A$, we also derive an explicit QTT representation of $A^{-1}$. The latter can be used, for instance, to overcome stability issues arising when numerically solving differential equations with periodic boundary conditions in the QTT format.