THERMAL, INTERFACIAL, AND APPLICATION PROPERTIES OF PEA PROTEIN MODIFIED WITH HIGH INTENSITY ULTRASOUND

The overall objective of the study was to investigate different food ingredient conditions and ultrasound treatment on pea protein in terms of surface morphology and thermal characteristics. The motivation of this work was based on previous studies focusing on non-chemical physical modifications of plant proteins and the increasing demand for functional alternative proteins. Ultrasonication time and amplitude, pH, protein concentration, and salt concentration all influenced the thermal and interfacial properties of pea protein. Ultrasound treatment altered the quaternary and tertiary structure of the storage protein and disrupted non-covalent bonds. The structural altercations and a reduction in particle size led to improved functionality. For foams generated at pH 5.0 with 4% (w/v) ultrasound treated protein, the foams had acceptable capacity and stability even when high levels of sugar (5% sucrose) and salt (0.6 M) were incorporated. An acceptable angel food cake simulation can be achieved by replacing egg white with ultrasound treated pea protein. Color and loaf height were different, but similar texture profiles were achieved. Ultrasound treatment significant improved the emulsifying capacity (up to 1.4 fold), emulsion stability, and creaming index compared to control samples (no ultrasound) over two weeks. The ultrasound treated emulsion yielded lower TBARS values, likely due to the change in exposed protein reactive groups. These findings demonstrate that ultrasound processing is an effective nonchemical method to change the structural and physiochemical properties of pea protein. Pea protein processed with this method might allow for the functionality in a bakery, dressings, or beverage products, which is appealing to many consumers and manufacturers

Reconstruction of Bandlimited Functions from Unsigned Samples

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases

On the inconsistency of the Bohm-Gadella theory with quantum mechanics

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page

Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions

In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as “quasi-parabolic.” This is the class of composition operators on H2 with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form φ(z)=z+ψ(z), where and (ψ(z))>>0. We especially examine the case where ψ is discontinuous at infinity. A new method is devised to show that this type of composition operator fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra