We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits combination of first-class and second-class constraints. derive the well-known Dirac equation fixing gauge in covariant manner, enabling fields to propagate accordingly. Notably, inherently possesses invariance under reparametrizations time. Consequently, vanishes, setting...

In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived remarkable identity: square of partition function fixed couplings is well approximated "wormhole" saddle plus "pair linked half-wormholes" saddle. It explains factorization decoupled systems. Here, derive an explicit formula fo...

Crystallization is an important separation technology used for the purification of products during their final stages of manufacturing. Novel semi-continuous and continuous crystallization process designs are receiving increasing attention in pharmaceutical industry due to significant advantages in terms of process, operation and costs. This dissertation aims to develop mathematical models for ...

Crystallization is an essential process for understanding a molecule's aggregation behavior. It provides basic information on crystals, including their nucleation and growth processes. Deoxyribonucleic acid (DNA) has become an interesting building material because of its remarkable properties for constructing various shapes of submicron-scale DNA crystals by self-assembly. The recently develope...

A new in-situ NMR strategy (termed CLASSIC NMR) for mapping the evolution of crystallization processes is reported, involving simultaneous measurement of both liquid-state and solid-state NMR spectra as a function of time. This combined strategy allows complementary information to be obtained on the evolution of both the solid and liquid phases during the crystallization process. In particular,...

Protein crystallography represents at present the most productive and most widely used method to obtain structural information on target proteins and protein-ligand complexes within the atomic resolution range. The knowledge obtained in this way is essential for understanding the biology, chemistry, and biochemistry of proteins and their functions but also for the development of compounds of hi...

The crystallization of undercooled Pd43Ni10Cu27P20 melts is studied under isothermal conditions and at constant heating and cooling rates. Investigations are carried out by fluxing the melt with B2O3 and without any fluxing material. The isothermal experiments allow us to determine the complete time–temperature-transformation diagram with a minimum crystallization time of about 200 s for the fl...