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In this paper, we prove that the quantum groups [Formula: see text] introduced by Mrozinski in [C. Mrozinski, Quantum groups of [Formula: see text] representation type, J. Noncommut. Geom. 8(1) (2014) 107–140] and their Hopf–Galois objects are twisted Calabi–Yau algebras, and give their Nakayama automorphisms explicitly.

In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the Poisson bracket of A is skew-symmetric, a Poisson version of the Shephard-Todd-Chevalley theorem is proved stating that the fixed Poisson subring A^G is skew-symmetric if and only if G is generated by reflections. For many other well-known families of quadratic Poisson algebras, we show that G contains limited or even no reflections. This kind of Poisson rigidity result ensures that the corresponding fixed Poisson subring A^G is not isomorphic to A as Poisson algebras unless G is trivial., Comment: Small revisions throughout. Remark 4.13 added courtesy of Akaki Tikaradze

Let $k$ be a field and let $R$ be a left noetherian $k$-algebra. The algebra $R$ satisfies the Dixmier-Moeglin equivalence if the annihilators of irreducible representations are precisely those prime ideals that are locally closed in the ${\rm Spec}(R)$ and if, moreover, these prime ideals are precisely those whose extended centres are algebraic extensions of the base field. We show that if $R$ and $S$ are two left noetherian $k$-algebras with ${\rm dim}_k(R), {\rm dim}_k(S), Comment: 13 pages

In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari-Rossi (2017)., Comment: 6 pages + references ; small changes following referee comments ; to appear in Proc. AMS

Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p 3 , which appear in the classification obtained in [20] . The list consists of 23 algebras together with two infinite families. We identify the Morita type of the algebra, and in almost all cases this is sufficient to clarify the structure of the cohomology ring.

Masuoka proved (Proc Am Math Soc 137(6):1925–1932, 2009) that a finite-dimensional irreducible Hopf algebra H in positive characteristic is semisimple if and only if it is commutative semisimple if and only if the Hopf subalgebra generated by all primitives is semisimple. In this note, we give another proof of this result by using Hochschild cohomology of coalgebras.

We define the universal quantum group $\mathcal{H}$ that preserves a pair of Hopf comodule maps, whose underlying vector space maps are preregular forms defined on dual vector spaces. This generalizes the construction of Bichon and Dubois-Violette (2013), where the target of these comodule maps are the ground field. We also recover the quantum groups introduced by Dubois-Violette and Launer (1990), by Takeuchi (1990), by Artin, Schelter, and Tate (1991), and by Mrozinski (2014), via our construction. As a consequence, we obtain an explicit presentation of a universal quantum group that coacts simultaneously on a pair of $N$-Koszul Artin-Schelter regular algebras with arbitrary quantum determinant., v2: To appear in Journal of Noncommutative Geometry

In this paper, the di ff erential graded (DG for short) Poisson adjoint action on M is introduced, where M is a DG Poisson module over a DG Poisson Hopf algebra A . As an application, we give a new DG poisson module structure over the DG Poisson Hopf algebra A , which depends heavily on the structure of A .

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson bracket on $Z$ is non-vanishing and is induced by an explicit potential. The ${\mathbb Z}_3 \times \Bbbk^\times$-orbits of symplectic cores of the Poisson structure are determined (where the group acts on $S$ by algebra automorphisms). In turn, this is used to analyze the finite-dimensional quotients of $S$ by central annihilators: there are 3 distinct isomorphism classes of such quotients in the case $(n,3) \neq 1$ and 2 in the case $(n,3)=1$, where $n$ is the order of the elliptic curve automorphism associated to $S$. The Azumaya locus of $S$ is determined, extending results of Walton for the case $(n,3)=1$.

For a class of parametric perturbed problems, we use a rational spectral method of barycenter with sinh transformation. By using sinh transform, more Chebyshev points are mapped to the singularity of the solution interval. Then, in order to calculate the mesh parameters of boundary layer width after sinh transformation and the parameters in the problem, this paper designs a nonlinear optimization with the objective function as the minimum error. In order to solve the optimization problem, we choose particle swarm optimization algorithm to solve the problem. Finally, through numerical experiments, it is found that particle swarm optimization (PSO) algorithm has significant advantages in solving such problems.

Let $H$ be a Hopf algebra that is $\mathbb Z$-graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of $H$ to be a Zhang twist of $H$. In particular, we introduce the notion of a twisting pair for $H$ such that the Zhang twist of $H$ by such a pair is a 2-cocycle twist. We use twisting pairs to describe twists of Manin's universal quantum groups associated to quadratic algebras and provide twisting of solutions to the quantum Yang-Baxter equation via the Faddeev-Reshetikhin-Takhtajan construction., Comment: In this version, we have updated references throughout our paper (to appear)

For any differential graded (DG for short) Poisson algebra $A$ given by generators and relations, we give a "formula" for computing the universal enveloping algebra $A^e$ of $A$. Moreover, we prove that $A^e$ has a Poincar\'e-Birkhoff-Witt basis provided that $A$ is a graded commutative polynomial algebra. As an application of the PBW-basis, we show that a DG symplectic ideal of a DG Poisson algebra $A$ is the annihilator of a simple DG Poisson $A$-module, where $A$ is the DG Poisson homomorphic image of a DG Poisson algebra $R$ whose underlying algebra structure is a graded commutative polynomial algebra., Comment: 26 pages. Any comments are welcome!

We focus on the classification of pointed p3-dimensional Hopf algebras H over any algebraically closed field of prime characteristic p > 0. In particular, we consider certain cases when the group of grouplike elements is of order p or p2, that is, when H is pointed but is not connected nor a group algebra. The structures of the associated graded algebra gr H are completely described as bosonizations of graded braided Hopf algebras over group algebras, and most of the lifting structures of H are given. This work provides many new examples of (parametrized) non-commutative, non-cocommutative finite-dimensional Hopf algebras in positive characteristic.

It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson enveloping algebra of a double Poisson-Ore extension., 15 pages

Let H and L be two Hopf algebras such that their comodule categories are monoidally equivalent. We prove that if H is a twisted Calabi–Yau (CY) Hopf algebra, then L is a twisted CY algebra when it is homologically smooth. In particular, if H is a Noetherian twisted CY Hopf algebra and L has finite global dimension, then L is a twisted CY algebra. The authors sincerely thank the referee for his/her valuable comments and suggestions that helped them to improve the paper quite a lot. Wang and Yu are grateful to the Department of Mathematics of Zhejiang Normal University for the hospitality they received during a visit in summer 2016. Wang is supported by AMS-Simons travel grant. Yu is supported by grants from NSFC (No. 11301126, No. 11571316, No. 11671351).

In support variety theory, representations of a finite dimensional (Hopf) algebra $A$ can be studied geometrically by associating any representation of $A$ to an algebraic variety using the cohomology ring of $A$. An essential assumption in this theory is the finite generation condition for the cohomology ring of $A$ and that for the corresponding modules. In this paper, we introduce various approaches to study the finite generation condition. First, for any finite dimensional Hopf algebra $A$, we show that the finite generation condition on $A$-modules can be replaced by a condition on any affine commutative $A$-module algebra $R$ under the assumption that $R$ is integral over its invariant subring $R^A$. Next, we use a spectral sequence argument to show that a finite generation condition holds for certain filtered, smash and crossed product algebras in positive characteristic if the related spectral sequences collapse. Finally, if $A$ is defined over a number field over the rationals, we construct another finite dimensional Hopf algebra $A'$ over a finite field, where $A$ can be viewed as a deformation of $A'$, and prove that if the finite generation condition holds for $A'$, then the same condition holds for $A$., 30 pages, to appear J. Algebra

We study the representation theoretic results of the binary cubic generic Clifford algebra $\mathcal C$, which is an Artin-Schelter regular algebra of global dimension five. In particular, we show that $\mathcal C$ is a PI algebra of PI degree three and compute its point variety and discriminant ideals. As a consequence, we give a necessary and sufficient condition on a binary cubic form $f$ for the associated Clifford algebra $\mathcal C_f$ to be an Azumaya algebra., to appear Algebr. Represent. Theory

We study the Zariski cancellation problem for Poisson algebras asking whether $A[t]\cong B[t]$ implies $A\cong B$ when $A$ and $B$ are Poisson algebras. We resolve this affirmatively in the cases when $A$ and $B$ are both connected graded Poisson algebras finitely generated in degree one without degree one Poisson central elements and when $A$ is a Poisson integral domain of Krull dimension two with nontrivial Poisson bracket. We further introduce Poisson analogues of the Makar-Limanov invariant and the discriminant to deal with the Zariski cancellation problem for other families of Poisson algebras., Final version

In this paper, we provide some topological criteria for the Poisson Dixmier-Moeglin equivalence for $A$ in terms of the poset $({\rm P. spec A}, \subseteq)$ and the symplectic leaf or core stratification on its maximal spectrum. In particular, we prove that the Zariski topology of the Poisson prime spectrum and of each symplectic leaf or core can detect the Poisson Dixmier-Moeglin equivalence for any complex affine Poisson algebra. Moreover, we generalize the weaker version of the Poisson Dixmier-Moeglin equivalence for a complex affine Poisson algebra proved in [J. Bell, S. Launois, O.L. S\'anchez, and B. Moosa, Poisson algebras via model theory and differential algebraic geometry, J. Eur. Math. Soc. (JEMS), 19(2017), no. 7, 2019-2049] to the general context of a commutative differential algebra., Comment: 29 pages, to appear Israel J. Math

We investigate homological and ring-theoretic properties of universal quantum linear groups that coact on Artin-Schelter regular algebras A(n) of global dimension 2, especially with central homological codeterminant (or central quantum determinant). As classified by Zhang, the algebras A(n) are connected \N-graded algebras that are finitely generated by n indeterminants of degree 1, subject to one quadratic relation. In the case when the homological codeterminant of the coaction is trivial, we show that the quantum group of interest, defined independently by Manin and by Dubois-Violette and Launer, is Artin-Schelter regular of global dimension 3 and also skew Calabi-Yau (homologically smooth of dimension 3). For central homological codeterminant, we verify that the quantum groups are Noetherian and have finite Gelfand-Kirillov dimension precisely when the corresponding comodule algebra A(n) satisfies these properties, that is, if and only if n=2. We have similar results for arbitrary homological codeterminant if we require that the quantum groups are involutory. We also establish conditions when Hopf quotients of these quantum groups, that also coact on A(n), are cocommutative., v4: 25 pages. To appear in Math Z

In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra., Comment: Accepted by Science China Mathematics

Let $p$, $q$ be two distinct primes. We consider pointed Hopf algebras of dimension $pq$ over an algebraically closed field of characteristic $p$. We compute higher Frobenius-Schur indicators of these Hopf algebras through the associated graded Hopf algebras with respect to their coradical filtrations. The resulting indicators are gauge invariants for the monoidal representation categories of these algebras.

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p, Comment: 7 pages; to appear in Bulletin of the London Mathematical Society

To study hypoglycemic effects of different mulberry leaf extracts on diabetic mice.STZ-induced diabetic mice were intragastricly administrated with different mulberry leaf extracts( water extracts: 800 mg/kg, ethanol extracts: 500 mg/kg, water extracts + ethanol extracts: low dose 150 mg/kg, high dose300 mg/kg) and positive control group( melbine: 227. 5 mg/kg). Four weeks later, serum glucose levels, insulin levels, antioxidase activities were tested. Liver and pancreas pathological changes were observed by HE staining.Compared with model group, each mulberry leaf extracts group could decrease serum glucose and insulin levels and increase antioxidase activities. The mixture of water extracts and ethanol extracts at high dose showed the most obvious effects. In this group, serum glucose levels, insulin levels, insulin resistance index and insulin sensitivity index were 61. 0%, 64. 1%, 42. 9% and 1. 18 times of those in the model group( P0. 05), and no significant differences were found between this group and the positive group( P0. 05).The mixture of mulberry leaf water and ethanol extracts showed synergistic hypoglycemic effects by increasing antioxidase activities, repairing pancrea and liver oxidative damages, and improving insulin resistance status.

Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is module-finite over its center Z; thus, S is PI. Our first result is the construction of a Poisson Z-order structure on S such that the induced Poisson bracket on Z is non-vanishing. We also provide the explicit Jacobian structure of this bracket, leading to a description of the symplectic core decomposition of the maximal spectrum Y of Z. We then classify the irreducible representations of S by combining (1) the geometry of the Poisson order structures, with (2) algebro-geometric methods for the elliptic curve attached to S, along with (3) representation-theoretic methods using line and fat point modules of S. Along the way, we improve results of Smith and Tate obtaining a description the singular locus of Y for such S. The classification results for irreducible representations are in turn used to determine the zero sets of the discriminants ideals of these algebras S., Comment: v2: 52 pages, to appear in Selecta Mathematica

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair associated with these extensions, we construct a cohomology group, which classifies all the extensions up to equivalence. Moreover, we present a $1$-$1$ correspondence between the isomorphism classes and a group quotient of the cohomology group deleting some exceptional points, where the group respects the automorphisms of the abelian matched pair and the exceptional points represent those restricted Lie algebra extensions., 27 pages, any comment is welcome

We continue the first and second authors' study of $q$-commutative power series rings $R=k_q[[x_1,\ldots,x_n]]$ and Laurent series rings $L=k_q[[x^{\pm 1}_1,\ldots,x^{\pm 1}_n]]$, specializing to the case in which the commutation parameters $q_{ij}$ are all roots of unity. In this setting, $R$ is a PI algebra, and we can apply results of De Concini, Kac, and Procesi to show that $L$ is an Azumaya algebra whose degree can be inferred from the $q_{ij}$. Our main result establishes an exact criterion (dependent on the $q_{ij}$) for determining when the centers of $L$ and $R$ are commutative Laurent series and commutative power series rings, respectively. In the event this criterion is satisfied, it follows that $L$ is a unique factorization ring in the sense of Chatters and Jordan, and it further follows, by results of Dumas, Launois, Lenagan, and Rigal, that $R$ is a unique factorization ring. We thus produce new examples of complete, local, noetherian, noncommutative, unique factorization rings (that are PI domains).

We compute higher Frobenius-Schur indicators of Radford algebras in positive characteristic and find minimal polynomials of these linearly recursive sequences. As a result of Kashina, Montgomery and Ng, we obtain gauge invariants for the monoidal categories of representations of Radford algebras., Accepted for publication by Involve, a journal of mathematics. The results in this paper were partially obtained from an undergraduate research project

In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras are discussed., 15 pages. Any comments are welcome!

The notion of $n$-th indicator for a finite-dimensional Hopf algebra was introduced by Kashina, Montgomery and Ng as gauge invariance of the monoidal category of its representations. The properties of these indicators were further investigated by Shimizu. In this short note, we show that the indicators appearing in positive characteristic all share the same sequence pattern if we assume the coradical of the Hopf algebra is a local Hopf subalgebra., Comment: 7 pages; to appear in Archiv der Mathematik

Over a field of prime characteristic $p>2$, we prove that the cohomology rings of some pointed Hopf algebras of dimension $p^3$ are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional Hopf algebras in positive characteristic, and include bosonizations of Nichols algebras of Jordan type in a general setting as well as their liftings when $p=3$. Our techniques are applications of twisted tensor product resolutions and Anick resolutions in combination with May spectral sequences., 29 pages

In this paper, we show that the twisted Poincar\'e duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of a unimodular Poisson algebra in terms of its Poisson Picard group. We also achieve twisted Poincar\'e duality for Hochschild (co)homology of Poisson bimodules using rigid dualizing complex. For a smooth Poisson affine variety with the trivial canonical bundle, we prove that its enveloping algebra is a Calabi-Yau algebra if the Poisson structure is unimodular., Comment: 26 pages, any comment is welcome

For finite-dimensional Hopf algebras, their classification in characteristic $0$ (e.g. over $\mathbb{C}$) has been investigated for decades with many fruitful results, but their structures in positive characteristic have remained elusive. In this paper, working over an algebraically closed field $\mathbf{k}$ of prime characteristic $p$, we introduce the concept, called Primitive Deformation, to provide a structured technique to classify certain finite-dimensional connected Hopf algebras which are almost primitively generated; that is, these connected Hopf algebras are $p^{n+1}$-dimensional, whose primitive spaces are abelian restricted Lie algebras of dimension $n$. We illustrate this technique for the case $n=2$. Together with our preceding results in arXiv:1309.0286, we provide a complete classification of $p^3$-dimensional connected Hopf algebras over $\mathbf{k}$ of characteristic $p>2$., 38 pages, 9 tables. We expanded and formalized our original version to a structured technique called Primitive Deformation, applicable in the classification of Hopf algebras in positive characteristic. We changed the title to fit in this new context. Comments and suggestions are welcome

For a Poisson algebra $A$, by exploring its relation with Lie-Rinehart algebras, we prove a Poincar\'e-Birkoff-Witt theorem for its universal enveloping algebra $A^e$. Some general properties of the universal enveloping algebras of Poisson Hopf algebras are studied. Given a Poisson Hopf algebra $B$, we give the necessary and sufficient conditions for a Poisson polynomial algebra $B[x; \alpha, \delta]_p$ to be a Poisson Hopf algebra. We also prove a structure theorem for $B^e$ when $B$ is a pointed Poisson Hopf algebra. Namely, $B^e$ is isomorphic to $B#_\sigma \mathcal{H}(B)$, the crossed product of $B$ and $\mathcal{H}(B)$, where $\mathcal{H}(B)$ is the quotient Hopf algebra $B^e/B^eB^+$., Comment: 37 pages. Reference updated

For a Poisson algebra $A$, by studying its universal enveloping algebra $A^{pe}$, we prove a duality theorem between Poisson homology and cohomology of $A$.

The form of nitrogen (N) [e.g., nitrate (NC3 ‐) and ammonium (NH4 +)] available to plants affects many growth processes, including mineral nutrient acquisition. The objective of this study was to assess the effects of N form on the accumulation and partitioning of mineral nutrients in wheat. Two species of spring wheat (Triticum aestivum L. cv. Len and Triticum durum Desf. cv. Inbar) were grown hydroponically in the greenhouse with N supplied as either all NO3 ‐, or all NH4 +, or an equal mixture of the two forms (mixed N). Plants were harvested after 21 days of growth, divided into shoots and roots and each part analyzed for nine mineral elements [phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), iron (Fe), manganese (Mn), zinc (Zn), copper (Cu), and boron (B)]. The accumulation and partitioning of the mineral nutrients was dependent on the wheat species, the N form, and the nature of the ion. Inbar plants always accumulated more of each element than did Len. Compared with all NO3 ‐ n...

Let $p$ be a prime, $k$ be an algebraically closed field of characteristic $p$. In this paper, we provide the classification of connected Hopf algebras of dimension $p^3$, except the case when the primitive space of the Hopf algebra is two dimensional and abelian. Each isomorphism class is presented by generators $x, y, z$ with relations and Hopf algebra structures. Let $\mu$ be the multiplicative group of $(p^2+p-1)$-th roots of unity. When the primitive space is one-dimensional and $p$ is odd, there is an infinite family of isomorphism classes, which is naturally parameterized by $A_{k}^1/\mu$., Comment: 32 pages, no figures

We prove that a finite-dimensional cocommutative Hopf algebra $H$ is local, if and only if the subalgebra generated by the first term of its coradical filtration $H_1$ is local. In particular if $H$ is connected, $H$ is local if and only if all the primitive elements of $H$ are nilpotent., Comment: 11 pages, no figures

Supplying wheat plants with mixtures of NO 3 - and NH 4 + increases growth and tiller production, but the physiological basis is unclear. Our objectives were to evaluate the roles for cytokinins and N use (e.g., accumulation, distribution, and utilization of absorbed N to produce tillers) in eliciting this response. Two species of spring wheat (Triticum aestivum L. cv. Len and Triticum durum Desf. cv. Inbar) were grown hydroponically in the greenhouse with N supplied as all NO 3 - , all NH 4 + , or an equal mixture of each form. In one experiment, the synthetic cytokinin N 6 -benzylaminopurine (100 μM) was applied repeatedly (a total of five times) to the shoots during tiller initiation and development, while in another, xylem exudate was collected from cut stumps during the early stages of tiller development. Plants not sprayed with cytokinins produced more tillers and accumulated more N when grown with mixed N than with either N form alone. Cytokinin sprays did not affect tillering of mixed N plants but increased tillers in all-NO 3 - -grown or all-NH 4 + -grown plants to levels close to that obtained with mixed N. For unsprayed plants, the presence of NH 4 + increased the shoot/root ratio, the proportion of N in the shoot, and the efficiency with which absorbed N was used to produce tillers, compared with plants grown with all NO 3 - . Exogenous cytokinin appeared to mimic the effects of mixed N (and in some cases NH 4 + ) in altering the distribution and use of N by the plant. In addition, plants grown with mixed N or all NH 4 + exhibited higher concentrations and mass transfer of cytokinins in the xylem than those supplied with all NO 3 - . These data are consistent with the interpretation that mixed N enhancement of tillering in wheat is due to increased synthesis of cytokinins, induced in part by use of NH 4 + -N.

Let $p$ be a prime. We complete the classification on pointed Hopf algebras of dimension $p^2$ over an algebraically closed field $k$. When $\text{char}k \neq p$, our result is the same as the well-known result for $\text{char}k=0$. When $\text{char}k=p$, we obtain 14 types of pointed Hopf algebras of dimension $p^2$, including a unique noncommutative and noncocommutative type., 10 pages, no figures

When grown with mixtures of nitrate‐nitrogen (NO3‐N) and ammonium‐nitrogen (NH4‐N) (mixed N) spring wheat (Triticum aestivum L.) plants develop higher order tillers and produce more grain than when grown with only NO3. Because similar work is lacking for winter wheat, the objective of this study was to examine the effect of N form on tillering, nutrient acquisition, partitioning, and yield of winter wheat. Plants of three cultivars were grown to maturity hydroponically with nutrient solutions containing N as either all NO3, all NH4, or an equal mixture of both forms. At maturity, plants were harvested; separated into shoots, roots, and grain; and each part analyzed for dry matter and chemical composition. While the three cultivars varied in all parameters, mixed N plants always produced more tillers (by a range of 16 to 35%), accumulated more N (28 to 61%), phosphorus (P) (22 to 80%), and potassium (K) (11 to 89%) and produced more grain (33 to 60%) than those grown with either form alone. Althou...

Growth and yield of wheat is enhanced when plants are provided with mixtures of NO 3 and NH 4 , compact with either form alone. The objective of this experiment was to further evaluate the effects of N form on growth and tillering of wheat, with particular attention to tiller phenology, root morphology, and N uptake. Two species of spring wheat (Triticum durum Desf. cv. Inbar and Triticum aestivum L. cv. Len) were grown in the greenhouse with five different ratios of NO 3 -N and NH 4 -N (100/0, 75/25, 50/50, 25/75, 0/100) (.)

In hydroponics, cereal crop growth is usually enhanced when the nutrient media contains both nitrate and ammonium compared to either form separately. Identification of genotypic variation between two spring wheat cultivars (Triticum aestivum cv. Len, and Triticum durum cv. Inbar) in their magnitude of growth response to mixed N permits a comparative evaluation of metabolic processes underlying enhanced growth from utilization of N mixtures. The objective of this study was to determine if the additional mixed N‐induced growth, and the difference in response between cultivars, is associated with the uptake or partitioning of N, P, or K during the seedling stage of development. Plants of Len and Inbar were grown hydroponicaily for 21 days in nutrient solutions containing N either as all nitrate or as a 50/50 mixture of nitrate and ammonium. The mean of three experiments showed that whole plant dry weight increased 19% for Len and 41 % for Inbar when the plants were supplied with the N mixture compar...