A major problem with reduced-fat cheese is the difficulty in attaining the characteristic flavor and texture of typical full-fat versions. Some previous studies have suggested that high hydrostatic pressure (HHP) can accelerate the ripening of full-fat cheeses. Our objective was to investigate the effect of HHP on reduced-fat (~7.3% fat) Cheddar cheese, with the goal of improving its flavor and texture. We used a central composite rotatable design with response surface methodology to study the effect of pressure and holding time on the rheological, physical, chemical, and microbial characteristics of reduced-fat Cheddar cheese. A 2-level factorial experimental design was chosen to study the effects of the independent variables (pressure and holding time). Pressures were varied from around 50 to 400 MPa and holding times ranged from 2.5 to 19.5 min. High pressure was applied 1 wk after cheese manufacture, and analyses were performed at 2 wk, and 1, 3, and 6 mo. The insoluble calcium content as a percentage of total Ca in cheeses were not affected by pressure treatment. Pressure applications ≥ 225 MPa resulted in softer cheese texture during ripening. Pressures ≥ 225 MPa increased melt, and resulted in higher maximum loss tangent values at 2 wk. Pressure treatment had a greater effect on cheese microbial and textural properties than holding time. High-pressure-treated cheeses also had higher pH values than the control. We did not observe any significant difference in rates of proteolysis between treatments. In conclusion, holding times of around 5 min and pressures of ≥ 225 MPa could potentially be used to improve the excessively firm texture of reduced-fat cheese.

In the present paper, we define the difference sequence space r q (p, Δ ), which is defined as follows:where r q (p) is the Riesz sequence space given by Altay and Başar. We give some topological properties and compute the α−, β − duals of this space.

ABSTRACT. In this paper, we introduce the Euler sequence space e r (p) of nonabsolute type and prove that the spaces e r (p) and l(p) are linearly isomorphic. Besides this, we compute the α-, β-and γ-duals of the space e r (p (p). Finally, we define a modular on the Euler sequence space e r (p) and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space e r (p) has property (H) but it is not rotund (R).

In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings on modular spaces endowed with a graph. The existence of fixed and common points of mappings satisfying generalized contractive conditions of integral type is also obtained in such spaces. Some examples are presented to support the results obtained herein. Our results generalize and extend various comparable results in the existing literature. MSC: 47H10; 54H25; 54E50

Jachymski (Proc. Am. Math. Soc. 136:1359Soc. 136: -1373Soc. 136: , 2008) gave a modified version of a Banach fixed point theorem on a metric space endowed with a graph. The aim of this paper is to present fixed point results of mappings satisfying integral type contractive conditions in the framework of modular spaces endowed with a graph. Some examples are presented to support the results proved herein. Our results generalize and extend various comparable results in the existing literature. MSC: 47H10; 54H25; 54E50