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In this paper, it is shown that every nonlinear bijective map ψ preserving mixed Jordan triple η-products with η ≠ − 1 from a factor von Neumann algebra M with dim M > 1 into another factor von Neumann algebra N with dim N > 1 is additive. Also, for α ∈ { − 1 , 1 } , we establish that α ψ is a linear *-isomorphism, and is a conjugate linear *-isomorphism only when η ∈ R . [ABSTRACT FROM AUTHOR]

Let be an ∗-algebra and k ∈ ℤ + . For A , B ∈ , the product defined by ∗ [ A , δ A (B) λ ∗ ] k = ∗ [ A , ∗ [ A , δ A (B) λ ∗ ] k − 1 ] 1 , where ∗ [ A , δ A (B) λ ∗ ] 0 = δ A (B) λ ∗ and ∗ [ A , δ A (B) λ ∗ ] 1 = A δ A (B) λ ∗ − δ A (B) λ ∗ A ∗ , is called λ - k -skew Lie product of A and B , where δ A (B) λ ∗ = A B − λ B A ∗ . This paper discusses some useful characteristics of λ - k -skew Lie products on prime ∗-algebras. Moreover, we investigate the effects of an additive map ϕ on with a λ - k -skew Lie product. [ABSTRACT FROM AUTHOR]

Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k. [ABSTRACT FROM AUTHOR]

Let 풜 be a prime ∗-algebra. For any A , B ∈ A , a product A ⋆ B = A ⁢ B * + B ⁢ A * is called a bi-skew Jordan product. In this paper, it is shown that every multiplicative bi-skew Jordan triple derivation is an additive ∗-derivation on a prime ∗-algebra. [ABSTRACT FROM AUTHOR]

The invention of smart low-power devices and ubiquitous Internet connectivity have facilitated the shift of many labour-intensive jobs into the digital domain. The shortage of skilled workforce and the growing food demand have led the agriculture sector to adapt to the digital transformation. Smart sensors and systems are used to monitor crops, plants, the environment, water, soil moisture, and diseases. The transformation to digital agriculture would improve the quality and quantity of food for the ever-increasing human population. This paper discusses the security threats and vulnerabilities to digital agriculture, which are overlooked in other published articles. It also provides a comprehensive review of the side-channel attacks (SCA) specific to digital agriculture, which have not been explored previously. The paper also discusses the open research challenges and future directions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the behavior of prime rings involving skew derivations with m-potent commutators on Lie ideals. In addition, we provide an example that shows that we cannot expect the same conclusion in case of semiprime rings. Also, we prove some other related results and present some open problems. [ABSTRACT FROM AUTHOR]

Let ℜ be a ring with center Z(ℜ). In this paper, we study the higher-order commutators with power central values on rings and algebras involving generalized derivations. Motivated by [A. Alahmadi, S. Ali, A. N. Khan and M. Salahuddin Khan, A characterization of generalized derivations on prime rings, Comm. Algebra 44 2016, 8, 3201–3210], we characterize generalized derivations and related maps that satisfy certain differential identities on prime rings. Precisely, we prove that if a prime ring of characteristic different from two admitting generalized derivation 𝔉 such that ([𝔉(sm)sn + sn𝔉(sm), sr]k)l ∈ Z(ℜ) or every s ∈ ℜ, then either 𝔉(s) = ps for every s ∈ ℜ or ℜ satisfies s4 and 𝔉(s) = sp for every s ∈ ℜ and p ∈ 𝔘, the Utumi quotient ring of ℜ. As an application, we prove that any spectrally generalized derivation on a semisimple Banach algebra satisfying the above mentioned differential identity must be a left multiplication map. [ABSTRACT FROM AUTHOR]

Motivated by Dar and Ali's [9] elegant work's, the goal of the paper is to study nth power *-property in rings with involution and its related problems. In fact, the main result of this paper gives conditions which ensure that an additive map d : R → R satisfying nth power *-property must be X-inner. As an application, we characterize additive map F : R → R such that F (x n) = F (x) (x ∗) n − 1 + ∑ i = 1 n − 1 x i d (x) (x ∗) n − i − 1 for all x ∈ R. where d : R → R is an additive map satisfying nth power *-property. These results provide the affirmative answer to the open problem (see Problem 3.3 [9]). [ABSTRACT FROM AUTHOR]

Let 1 < k and m, k 2 Z+. In this manuscript, we analyse the action of (semi)-prime rings satisfying certain differential identities on some suitable subset of rings. To be more specific, we discuss the behaviour of the semiprime ring R satisfying the differential identities ([d([s, t]m), [s, t]m])k = [d([s, t]m), [s, t]m] for every s, t 2 R. [ABSTRACT FROM AUTHOR]

Let A be unital prime Banach algebra over ℝ or ℂ with centre and G1, G2 be open subsets of be a continuous linear generalized skew derivation, and be a continuous linear map. We prove that must be commutative if one of the following conditions holds: For each a ∈ G1, b ∈ G2, there exists an integer m ∈ Z>1 depending on a and b such that either. For each a ∈ G1, b ∈ G2, there exists an integer m ∈ Z>1 depending on a and b such that either. These results generalize a number of theorems of this type. In particular, as an application, we give an affirmative answer to some questions posed in [21]. [ABSTRACT FROM AUTHOR]

Let R be a ring with involution and let α and β be endomorphisms of R. In this paper we characterise generalised Jordan (α, β)-higher derivations and related maps on (semi)-prime rings with involution. As consequences of our main theorems, many known results can be either generalised or deduced. [ABSTRACT FROM AUTHOR]

We address various topologies (de Bruijn, chordal ring, generalized Petersen, and meshes) in various ways (isometric embedding, embedding up to scale, and embedding up to a distance) in a hypercube or a half-hypercube. Example of obtained embeddings: infinite series of hypercube embeddable bubble sort and double chordal rings topologies, as well as of regular maps. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A map δ : S ⊆ A → A is called a strong commutativity preserving (SCP) on S if [ δ (x) , δ (y) ] = [ x , y ] for all x , y ∈ S , where A is a Banach algebra over C or R and S is a nonempty subset of A . The main goal of this manuscript is to investigate the SCP skew derivations on Banach algebra A and we obtain action of skew derivations on rings and the structure of prime Banach algebras. [ABSTRACT FROM AUTHOR]