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Consider an open quantum system S , interacting with its environment E. Whether the reduced dynamics of the system can be given by a linear map, or not, is an important subject, in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. They have considered the case that both the system and the environment are finite dimensional. Their framework can be generalized to include the case that the environment is infinite dimensional too. In this paper, after demonstrating this generalization, we discuss the role of the convexity of the set, of possible initial states of the system-environment, in their framework. Next, we give a proof for the existence of the operator sum representation, for arbitrary linear Hermitian map. This proof enables us to prove the Choi-Jamiołkowski and the Jamiołkowski isomorphisms, straightforwardly.

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We show that there is an affine order isomorphism between completely positive maps from a C*-algebra A to the C*-algebra L(H) of all bounded linear operators on a Hilbert space H, u-covariant with respect to a C*-dynamical system (G, a,A) and u-covariant completely positive maps from the crossed product A ×a G to L(H), which preserves the Lebesgue decomposition.

Let A and B be standard operator algebras on Banach spaces X and Y, respectively. Let ϕ, : A →,B be a bijective map. In this paper, we show that ϕ,is completely preserving quadratic operator in both directions if and only if ϕ,is 2-quadratic preserving operator in both directions and if and only if ϕ,is either an isomorphism or (in the complex case) a conjugate isomorphism.

Consider an open quantum system S, interacting with its environment E, and also an ancillary Hilbert space R. The reduced dynamics of the system S is given by a completely positive map, if the set S={ρSE} , of possible initial states of the system-environment, can be written as a steered set from a tripartite Markov state ƮRSE. In this paper, we call such steered states as Markovian states ρSE, and study a physical case, in which the reduced dynamics of the system can be completely positive, even when the initial states of the system-environment ρSE are non-Markovian.

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation semigroups is also obtained.

The notion of amalgamation of product systems has been introduced in [7] which generalize the concept of Skeide product, introduced by Skeide, of two product systems via a pair of normalized units. In this paper we show that amalgamation leads to a setup where a product system is generated by two subsystems and conversely whenever a product system is generated by two subsystems, it could be realized as an amalgamated product. We parameterize all contractive morphism from a Type I product system to another Type I product system and compute index of amalgamated product through contractive morphisms.

The specific activity of radionuclides in the soil of the Borujerd region using high purity Germanium detector (HPGe) was measured and the associated radiological hazards were calculated. The mean specific activity of radionuclides of Ra-226, Th-232, K-40, and Cs-137 in soil was obtained at 10.99±5.11, 35.36±4.44, 324.20±10.24, and 2.93±0.60 Bq.kg-1. These values were below the global average. Also, the value of basic radiological risk parameters, such as Raeq, AEDout, AEDint, Hex, Hin, and Iγ, ranged from 52.02 to 139.54 in Bq.kg-1, from 24.98 to 68.27 and from 42.90 to 117.22 in mSv.y-1, 122.57 to 334.93, 0.14 to 0.37, 0.16 to 0.40, and 0.27 to 1.04, respectively. The range of excess lifetime cancer risk (ELCR) value for the surrounding soil samples varied from 0.15×10-3 to 0.41×10-3, in which samples S4, S14, S24, S27, S28, S29, and S30 exceeded the global average of 0.29×10-3. A radiological map of the city of Borujerd was prepared using the GIS program. The study showed that the level of radioactivity in the Borujerd area did not exceed the critical value and is in line with the global results.

Background and Objectives: Detailed soil maps are an essential tool for achieving sustainable management. Despite advances in digital soil mapping and efforts to produce accurate maps, insufficient reliability of soil maps on many scales remains. Recent studies have focused primarily on remote sensing, which takes into account the characteristics of the subsurface of the soil. This study used a new interpolation method between subsurface characteristics and soil diagnostic properties to increase the accuracy of the prepared maps. In this study, the production of soil maps with two approaches including use of geomorphic surfaces as well as the interpolation of subsurface characteristics of the soil in the Chalous region were examined. Materials and Methods: The study area with an area of 100 hectares in Bandar village is one of the functions of Kelardasht section of Chalous city in Mazandaran province. The thickness or depth of the upper / lower boundary of characteristic horizons or characteristic soil characteristics was used as a criterion for distinguishing soil map units. According to the Comprehensive American Soil Classification System, there are six influential characteristics in the division of regional soils at the family level (Upper Combine horizon boundary, argillic horizon upper boundary, calcic horizon upper boundary, Malic horizon thickness, limestone or limestone thickness or the numerical interpolation of these features was used to generate thematic maps. The final soil map of the region was obtained by combining these six thematic maps. After mapping each of the soil properties separately, all the prepared maps were crossed and a map of homogeneous units was obtained. In order to study and describe the spatial structure of the variables, a semivariogram was used. The existence of data trend and heterogeneity was also examined. After preparing the change curves, the selection of the best models was done using cross-validation method and RMSS index. Results: In order to prepare the soil map using the geomorphic surface method, out of 20 soil units identified, 12 soil units were of the same type and 8 units were of the community type. However, all 20 map units obtained by interpolation of subsurface features were of the same type. This method had high accuracy in drawing the boundary between soil units. The main differences between this method and traditional methods are in the production of detailed soil maps, the use of supervised automatic interpolation instead of manual interpolation, and the use of a set of quantitative indicators. Conclusion: One of the major advantages of this method is the use of internal characteristics of the soil as an auxiliary variable along with other climatic factors, topography, living organisms, parent material and time. This study underscored the importance of the role of factor s in the SCORPAN model and showed that the internal properties of the soil, which are directly involved in soil classification, can be effectively used to separate soil units.