Abstract: Disclosed is a multi-constraint qubit allocation method and a quantum apparatus using the same. The method comprises generating an interaction graph representing a quantum circuit on the basis of the number of two-qubit gates, determining edge weights between connected nodes in the interaction graph by introducing a fitting coefficient for a decay effect, searching for an isomorphic part, layout graph, between target hardware and the interaction graph by graph matching, and performing frequency matching for a layout graph by searching for frequency allocated to each location of qubits by limiting unidirectional movement on each of an x-axis and a y-axis of a hardware plane of the target hardware to a range from ?1 to +1.

Abstract: Disclosed are positive electrode active materials, positive electrodes, and a rechargeable lithium battery including the same. Some of the positive electrode active materials include particles of a first positive electrode active material including lithium cobalt-based oxide, and particles of a second positive electrode active material including a layered lithium nickel-manganese-based composite oxide having a nickel content of greater than or equal to about 60 mol % based on 100 mol % of a total metal excluding lithium, wherein the first positive electrode active material or the second positive electrode active material includes a coating layer including yttrium.

Abstract: A positive electrode active material includes: a first positive electrode active material including a lithium nickel-manganese composite oxide having a nickel content of at least about 60 mol % based on a total metal excluding lithium and being in a form of secondary particles each including a plurality of primary particles; and a second positive electrode active material including a lithium nickel-manganese-based composite oxide having a nickel content of at least about 60 mol % based on a total metal excluding lithium and being in a form of single particles and a coating layer on the surface of the single particle and containing aluminum and yttrium, an aluminum content of the coating layer being about 0.1 mol % to about 2 mol % and an yttrium content of the coating layer being about 0.1 mol % to about 1 mol %, based on a total metal excluding lithium in the second positive electrode active material.

Abstract: A positive electrode active material, a method of preparing the same, a positive electrode and a rechargeable lithium battery including the same are provided. The positive electrode active material includes core particles including a lithium nickel-manganese-based composite oxide having a nickel content (e.g., amount) of greater than or equal to about 60 mol % based on 100 mol % of a total metal in the positive electrode active material excluding lithium, and a coating layer disposed on the surface of the core particles and including Al, Zr, and Mg.

Abstract: A positive electrode active material including a first positive electrode active material including a lithium nickel-manganese-based composite oxide having a nickel content of greater than or equal to about 60 mol % based on about 100 mol % of a total metal excluding lithium and including secondary particles made by agglomerating a plurality of primary particles wherein an average particle diameter (D50) of the secondary particle is about 10 ?m to about 20 ?m, a second positive electrode active material including a lithium nickel-manganese-based composite oxide having a nickel content of greater than or equal to about 60 mol % based on about 100 mol % of a total metal excluding lithium and including single particles wherein an average particle diameter (D50) of each of the single particles is about 2 ?m to about 8 ?m, and a third positive electrode active material includes particles including lithium transition metal phosphate.

Abstract: The present invention includes a jig for installing a protection member to a portable electronic device and a guide jig device including the same. The jig includes a main body and retaining members formed to be elastically deformed and coupled or connected to the main body while surrounding a mounting space in which the portable electronic device formed in the main body is inserted. The guide jig device is advantageous in that it can be used for a portable electronic device that is manufactured and sold in a size relatively greater than the size of the portable electronic device disclosed before its release.

Abstract: A continuous, quick measurement method of BOD, and an apparatus therefor is disclosed. The apparatus comprises a sample tank in which a sample is prepared suitably for the measurement, a reactor in which microorganisms maintain their activity, a medium reservoir which contains nutrients for the growth of the microorganisms, pumps for transferring liquids, and a microprocessor which controls the operation of all means including a magnetic stirrer for mixing the liquid in the reactor and diagnoses of the apparatus itself. Using the apparatus, the method comprises a continuous culture stage, an endogenous respiration stage, a endogenous respiration rate-measuring stage, a sample feeding stage and a BODq measuring stage. The apparatus can detect BOD in one hour and is very low in error rate. Further, because microorganisms can be continuously cultured, the apparatus is semi-permanent, easy to manage, low in cost and suitable to be operated at a treatment site.