UAM Iztapalapa

This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics are considered. Noether-like theorems relating one-parameter groups of transformations with canonical and noncanonical symmetries, are formulated, proved as well as illustrated with elementary examples.

Thermogravimetry coupled to Fourier-transform infrared spectroscopy (TGA/FTIR) was used to analyze the evolved gases from pyrolysis of four different lignocellulosic fibers (abaca, hemp, henequen, and coconut) that contain variable percentages of cellulose, hemicellulose and lignin. TGA results revealed that although the fibers exhibited different thermal stabilities (henequen had the highest decomposition temperature while coconut reported the lowest), the thermal decomposition pattern was similar as all samples displayed two degradation stages. By comparing representative spectra of the evolved gases at each stage for all-natural fibers, it was observed that during the first emission, the released gases were different and varied depending on fiber type. In contrast, during the second emission, similar spectra were obtained for all-natural fibers. Thus, it was found that during the first stage, abaca fibers release mainly carbon dioxide, hemp fibers evolve gases containing hydroxyl and carbonyl functionalities, whereas henequen and coconut ones produce carbon dioxide and gases that contain compounds possessing carbonyl and hydroxyl functional groups. During the second stage, all samples released carbon dioxide as well as compounds containing carbonyl, hydroxyl, and aliphatic functional groups.

We investigate how quantum mechanics restores confinement in Hamiltonian systems that are classically unstable and strongly chaotic. We focus on two quartic models: the Contopoulos Hamiltonian and the purely quartic x2y2 Yang-Mills Hamiltonian. Classical phase-space structure is characterized using Poincar & eacute; sections, Lyapunov exponents, and symmetry-line methods, revealing escape along diagonal channels in the Contopoulos case for negative coupling and along coordinate axes in the Yang-Mills case for positive coupling. Despite this classical unboundedness, the quantum x2y2 Yang-Mills Hamiltonian possesses a purely discrete spectrum. Using Lagrange-Mesh diagonalization, semiclassical reduction, and WKB quantization, we demonstrate that quantum-mechanically transverse zero-point motion generates an effective linear barrier along the escape channels, restoring confinement. High-precision numerical spectra and tube-projected eigenstates quantitatively confirm this mechanism. Our results establish a transparent semiclassical mechanism for quantum confinement beyond classical instability.

Degenerate quantum eigenspaces can support substantial changes in nodal geometry at fixed energy. We show that, for the two-dimensional isotropic harmonic oscillator, this restructuring is organized by the Hermite-constrained algebraic curve P_N(x,y)=0 appearing in every real shell state, ψ_N=e^-αr^2/2P_N(x,y). Finite singularities, P_N=∇ P_N=0, and projective degeneracies of the leading homogeneous part identify the strata where topology-changing events can occur. We combine these criteria with entropy diagnostics: the nodal-domain entropy S_dom, Cartesian mutual information I(x;y), and the entropic uncertainty sum S_r+S_p. The first three shells reveal a hierarchy: N=1 only rotates a nodal line; N=2 has a conic transition at b^2=2ac, sharply detected by S_dom but not by global entropies; and N=3 supports cubic close-branch regimes organized by the projective discriminant, with enhanced responses in S_dom and I(x;y). Thus algebraic stratification, rather than spectral ordering, organizes nodal geometry inside a degenerate eigenspace, while entropy diagnostics quantify probability redistribution and correlation. The framework suggests experimentally reconstructible signatures for real-phase Hermite–Gaussian structured light and approximately isotropic trapped motional systems.

Comparative studies report inconsistent peptide yields, bioactivities, and sensory outcomes for Alcalase across substrates, creating uncertainty about when it should be favored over other proteases. This study mapped research on hydrolysis of food proteins with Alcalase to quantify scientific output, organize thematic trends, and identify gaps relevant to peptide-based functional foods. A bibliometric analysis of Web of Science records (2004–2024) was performed in R (bibliometrix), using co-occurrence networks, temporal overlays, and conceptual mapping. The dataset comprised 203 documents from 78 sources, exhibiting a 10.3% annual growth rate and a 36.9% international co-authorship rate. Themes clustered around antioxidant and angiotensin-converting enzyme (ACE) inhibitory peptides, particularly in dairy and marine matrices, are supported by workflows combining Alcalase hydrolysis with size-guided ultrafiltration, RP-HPLC (Reverse Phase High-Performance Liquid Chromatography), and, more recently, in silico analyses and encapsulation studies. Recurrent limitations were identified: heterogeneous hydrolysates and uneven reporting that hinder sequence–activity correlations, gastrointestinal degradation and bitterness affecting applicability, and scale-up and purification choices influencing feasibility. The mapping clarified where Alcalase enables bioactive peptide generation and highlighted practical priorities, including protocol standardization and enzyme benchmarking, the integration of peptidomics and machine learning with targeted assays, and formulation-focused validation (encapsulation, stability, and delivery) to bridge in vitro activity to real-world use. These directions support the production of reproducible, application-ready peptide ingredients.