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Let A be a unital prime *-algebra (over the complex field C ) with a nontrivial projection. For any S 1 , S 2 , ... , S n ∈ A , define q 1 (S 1) = S 1 , q 2 (S 1 , S 2) = [ S 1 , S 2 ] ⋄ = S 1 S 2 − S 2 S 1 ∗ and q n (S 1 , S 2 , ... , S n) = [ q n − 1 (S 1 , S 2 , ... , S n − 1) , S n ] ⋄ for all integers n ≥ 3. In this article, it is shown that if a map ξ : A → A (not necessarily linear) satisfies ξ (q n (S 1 , S 2 , ... , S n)) = ∑ i = 1 n q n (S 1 , ... , S i − 1 , ξ (S i) , S i + 1 , ... , S n) (n ≥ 3) for all S 1 , S 2 , ... , S n ∈ A with S 1 ∗ S 2 ∗ ⋯ S n ∗ = 0 , then ξ is an additive *-derivation. Finally, this result is applied to standard operator algebras and factor von Neumann algebras. [ABSTRACT FROM AUTHOR]

Assume that is a unital algebra over a commutative unital ring ℛ and is an -bimodule. A trivial extension algebra ⋉ is defined as an ℛ -algebra with usual operations of ℛ -module × and the multiplication defined by (u 1 , s 1) (u 2 , s 2) = (u 1 u 2 , u 1 s 2 + s 1 u 2) for all u 1 , u 2 ∈ , s 1 , s 2 ∈. In this paper, we prove that under certain conditions every Jordan n -derivation Δ on ⋉ can be expressed as Δ = d + δ , where d is a derivation and δ is both a singular Jordan derivation and an antiderivation. As applications, we characterize Jordan n -derivations on triangular algebras and generalized matrix algebras. [ABSTRACT FROM AUTHOR]

Energy demand is rising over time in both developing and developed countries. Therefore, finding new sources of energy is a prime concern now. For this effort, this paper presents the pyrolysis of onion (Allium cepa) shells in a reactor with a fixed bed for generating alternative liquid fuel. This paper also compares alternative fuel characteristics, including higher heating value, viscosity, density, pour point, and flash point, with conventional petroleum fuels at optimal process conditions. The work adopted pyrolysis to produce liquid fuel at a temperature range of 400–550 °C and utilized LPG to provide a heat source. The liquid product (fuel oil) was collected, and non-condensable gas was flared. The liquid product was tested for various properties, and the results of the analyses show that alternative fuel has a higher heating value of 12.227 MJ/kg, density of 800 kg/m3, viscosity of 4.3 cP at 30 °C, pour point below −6.2 °C, and flash point around 137 °C, with a variation due to the volatile matters. To obtain favorable conditions for pyrolysis, some parameters, including bed temperature, sample quantity, average particle size, and operating time, were varied and analyzed. The physio-chemical properties made the alternative fuels isolated from conventional petroleum fuels due to the variation in distillation temperature. This work shows that the fuel oil generated from the pyrolysis of onion shells could be considered an alternative source of fuel. [ABSTRACT FROM AUTHOR]

Let 프 be a triangular ring and let p n ⁢ (U 1 , U 2 , ... , U n) denote the (n - 1) th commutator of elements U 1 , U 2 , ... , U n ∈ 프 . Suppose that ℕ is the set of nonnegative integers and 픏 = { ξ r } r ∈ ℕ is a sequence of additive mappings on 프 such that ξ 0 = i ⁢ d 프 , the identity mapping on 프 , and for each r ∈ ℕ , ξ r ⁢ (p n ⁢ (U 1 , U 2 , ... , U n)) = ∑ i 1 + i 2 + ⋯ + i n = r p n ⁢ (ξ i 1 ⁢ (U 1) , ξ i 2 ⁢ (U 2) , ... , ξ i n ⁢ (U n)) for all U 1 , U 2 , ... , U n ∈ 프 with U 1 ⁢ U 2 ⁢ ⋯ ⁢ U n = 0 . In this paper, it is shown that under certain conditions 픏 = { ξ r } r ∈ ℕ has the standard form, that is, there exist a higher derivation { d r } r ∈ ℕ on 프 and a family { h r } r ∈ ℕ of additive mappings h r : 프 → 풵 ⁢ (프) satisfying h r ⁢ (p n ⁢ (U 1 , U 2 , ... , U n)) = 0 for all U 1 , U 2 , ... , U n ∈ 프 with U 1 ⁢ U 2 ⁢ ⋯ ⁢ U n = 0 such that for each r ∈ ℕ , ξ r ⁢ (U) = d r ⁢ (U) + h r ⁢ (U) for all U ∈ 프 . [ABSTRACT FROM AUTHOR]

Aphids severely affect crop production by transmitting many plant viruses. Viruses are obligate intracellular pathogens that mostly depend on vectors for their transmission and survival. A majority of economically important plant viruses are transmitted by aphids. They transmit viruses either persistently (circulative or non‐circulative) or non‐persistently. Plant virus transmission by insects is a process that has evolved over time and is strongly influenced by insect morphological features and biology. Over the past century, a large body of research has provided detailed knowledge of the molecular processes underlying virus‐vector interactions. In this review, we discuss how aphid biology and morphology can affect plant virus transmission. © 2021 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]