Sylvester-polynomial-conjugate matrix equations unify many well-known versions and generalizations of the Sylvester matrix equation AX−XB=C which have a wide range of applications. In this paper, we ...present a general approach to Sylvester-polynomial-conjugate matrix equations via groupoids, vector spaces, and matrices over skew polynomial rings. The obtained results are applied to Sylvester-polynomial-conjugate matrix equations over complex numbers and quaternions. The main role in our approach is played by skew polynomial rings, which are well-known tools in algebra to provide examples of asymmetry between left-sided and right-sided versions of many ring objects.
The paper provides a complex, critical assessment of heavy metal soil pollution using different indices. Pollution indices are widely considered a useful tool for the comprehensive evaluation of the ...degree of contamination. Moreover, they can have a great importance in the assessment of soil quality and the prediction of future ecosystem sustainability, especially in the case of farmlands. Eighteen indices previously described by several authors (
I
geo
, PI, EF
, C
f
, PI
sum
, PI
Nemerow
, PLI, PI
ave
, PI
Vector
, PIN, MEC, CSI, MERMQ,
C
deg
, RI, mCd and ExF) as well as the newly published Biogeochemical Index (BGI) were compared. The content, as determined by other authors, of the most widely investigated heavy metals (Cd, Pb and Zn) in farmland, forest and urban soils was used as a database for the calculation of all of the presented indices, and this shows, based on statistical methods, the similarities and differences between them. The indices were initially divided into two groups: individual and complex. In order to achieve a more precise classification, our study attempted to further split indices based on their purpose and method of calculation. The strengths and weaknesses of each index were assessed; in addition, a comprehensive method for pollution index choice is presented, in order to best interpret pollution in different soils (farmland, forest and urban). This critical review also contains an evaluation of various geochemical backgrounds (GBs) used in heavy metal soil pollution assessments. The authors propose a comprehensive method in order to assess soil quality, based on the application of local and reference GB.
For any commutative semigroup
S
and positive integer
m
the power function
f
:
S
→
S
defined by
f
(
x
)
=
x
m
is an endomorphism of
S
. We partly solve the Lesokhin–Oman problem of characterizing the ...commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid
S
is a power function if and only if
S
is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup
S
with an idempotent is a power function if and only if
S
is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid
S
with 0, preserving 0 and 1, is a power function if and only if either
S
is a finite cyclic group with zero adjoined or
S
is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup
S
without idempotents is a power function if and only if
S
is a subsemigroup of the infinite cyclic semigroup.
A skew generalized power series ring
consists of all functions from a strictly ordered monoid
to a ring
whose support is artinian and narrow, with pointwise addition, and with multiplication given by ...convolution twisted by an action ω of the monoid
on the ring
.
Special cases of this ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal’cev–Neumann series rings, the “unskewed” versions of all of these, and generalized power series rings.
In this paper, we characterize the skew generalized power series rings
that are left (right) Archimedean domains in the case where the order
is total, or
is semisubtotal and the monoid
is commutative torsion-free cancellative, or
is trivial and
is totally orderable.
We also answer four open questions posed by Moussavi, Padashnik and Paykan regarding the rings in the title.
Purpose
Literature reported that soils characterized by heterogeneity would reveal the different direction of clay minerals transformation. Hence, in this study, four soils developed on menilite ...shales slope deposits were investigated to test if the clay minerals transformations in soils with varied calcium carbonate distribution would show multidirectional paths of clay mineral weathering, or if transformation of secondary phases in such stratified materials would reveal only one trajectory.
Methods
The separated clay fractions were analysed using X-ray diffractometry and Fourier-transform infrared spectroscopy. Geochemical analyses were performed using ICP-ES and ICP-MS after sample fusion with lithium borate and an alloy dissolution with nitric acid.
Results
Calcium carbonate did not influence the composition and transformation of clay minerals. Despite the fact that soils were characterized by different content and distribution of calcium carbonate within the solum and additionally indicated various morphological features, the mineralogical composition of clay fraction was very uniform. Among the secondary phases, chlorite, illite, vermiculite, kaolinite and mixed phases illite-smectite and vermiculite-chlorite were detected in all horizons.
Conclusions
The uniform composition of the clay minerals in the studied soils suggested that mass movement, which controlled the formation of slope covers, was probably of a similar character and intensity across the whole of the slope. Furthermore, it seems that the pedogenesis in all soils proceeded on the same scale of advancement. This was indicated by a similar degree of weathering of soil material and lack of depth-dependent weathering in the profiles, confirmed by values of weathering indices (CIA and ICV) as well as by micromorphologically visible, highly weathered coarse fragments. Moreover, weak intensity of the illuviation process within the homogeneous substrate could have resulted in the very uniform composition of clay minerals in the studied soils.
Seven soil profiles developed on calcium carbonate–rich slope deposits in the Polish Carpathians were studied in order to: i) determine the micromorphological features of heterogeneous soils formed ...in a carbonate depositional environment, and ii) track primary and secondary calcium carbonate forms and their distribution in such stratified soils. Three cases of soils with different arrangements of calcium carbonate were distinguished, controlled mostly by slope processes. For instance, the increasing content and random distribution of angular and subangular rock fragments found in the overall soil matrix and the irregular coarse: fine size limit suggested different intensities of accumulation and mixing of soil material transported along the slope. Slope processes, together with the calcium carbonate content, mineralogical characteristics and texture influenced the type and arrangement of the bfabric pattern. The calcium carbonate distribution within the soils, besides the obvious inheritance from parent material, was governed by the translocation and mixing of deposits on slopes. The climatic conditions prevailing in the area favour the development of secondary forms of calcium carbonate. However, only three of the seven studied profiles contained pedogenic forms of calcium carbonate, yet they were distributed randomly. The occurrence, distribution and preservation of secondary carbonates depended on the content of primary calcium carbonate and soil features such as texture. The transported material down the slope may indicate a very low content of primary calcium or lack thereof, hence its pedogenic forms could not be created.
Composts are considered to be one of the best soil amendments. However, the effects of composts with added polymeric materials on soil physical, hydraulic, and micromorphological properties have not ...been widely discussed. Changes in soil physical properties influence the numerous services that soils provide. We studied the impacts of composts with the addition of three different polymers (F1–F3) produced from polyethylene and thermoplastic corn starch on the physical, hydraulic, and micromorphological properties of two soils, a Cambic Phaeozem and a Luvic Phaeozem. Applying composts with polymers had limited or no significant effect on soil bulk density and porosity, but increased the field water capacity by 18%–82% and 3%–6% and the plant-available water content by 15%–23% and 4%–17% for the Cambic Phaeozem and Luvic Phaeozem, respectively. The application of composts with polymers had a greater effect on the Cambic Phaeozem than on the Luvic Phaeozem. It was suggested that the use of modified composts led to changes in soil physical properties and micromorphological features and this effect was dependent on the compost application rate. Composts made with the addition of composite synthetic and natural material-derived polymers during composting were found to be a composite mixture that can be successfully used in agriculture.
Let R be a ring, S a strictly ordered monoid, and ω:S→End(R) a monoid homomorphism. The skew generalized power series ring RS,ω is a common generalization of (skew) polynomial rings, (skew) power ...series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent series rings. We study the (S,ω)-Armendariz condition on R, a generalization of the standard Armendariz condition from polynomials to skew generalized power series. We resolve the structure of (S,ω)-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be (S,ω)-Armendariz, unifying and generalizing a number of known Armendariz-like conditions in the aforementioned special cases. As particular cases of our general results we obtain several new theorems on the Armendariz condition; for example, left uniserial rings are Armendariz. We also characterize when a skew generalized power series ring is reduced or semicommutative, and we obtain partial characterizations for it to be reversible or 2-primal.
Recently Wu, Wang and Teng introduced the division ring over conjugate product as a tool to investigate antilinear systems. In this paper we show that the division ring is a special case of a known ...construction of a right ring of fractions of a right Ore domain. We also investigate similarity and consimilarity of complex polynomials over conjugate product and characterize all the polynomials which are similar to a given polynomial of degree less than 3, solving partially a problem posed by Wu, Wang and Teng.
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