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Formal written replacement for で, marking a place, time, or field/domain. Common in reports, notices and academic writing; における modifies a following noun.
N + において／においては／においても；N + における + N
〜において / 〜における
"Leaving aside / without," removing something normally expected. With 〜を抜きにしては／抜きでは plus a negative it means "without X, Y would not happen." Neutral to slightly formal.
N + を抜きにして／は抜きにして；N + を抜きにしては／抜きでは + 否定
〜を抜きにして
"Based on / in accordance with," where the noun is a standard, rule, fact or data set that the action conforms to. Formal, common in legal, business and academic contexts.
N（規則・データ・事実）+ に基づいて／に基づき；N + に基づく／に基づいた + N
〜に基づいて
"Based on," naming the source material used to make something. Softer and broader than に基づいて: the material is raw input, not a rule to obey.
N + をもとに（して）；N + をもとにした + N
〜をもとに
"Putting (a feeling) into," used with emotion nouns such as 心, 感謝, 愛, 祈り. Slightly literary but common in letters, songs and everyday warm speech.
N（心・感謝・愛・祈り など感情の名詞）+ を込めて
〜をこめて
Formal "upon / at the time of" for an important undertaking one is about to begin. Used in speeches and business writing; the main clause states what is done in preparation or in that spirit.
N + に当たって／に当たり；V-dict + に当たって；N修飾は「に当たっての + N」
〜に当たって
"Concerning / surrounding," used for a topic that people argue, debate or compete over. Typical of news and formal writing; the main clause usually involves conflict or discussion.
N + をめぐって／をめぐり；N + をめぐる + N
〜をめぐって
"Along with / as a result of," for a change or event that brings another change with it. Formal written style, common in news and reports.
N + に伴って／に伴い；V-dict + に伴って；N + に伴う + N
〜に伴って
Literally "along" a line such as a river or road, and figuratively "in line with" a policy, plan or someone's wishes. Fairly formal, common in business.
N（道・川・方針・希望・計画）+ に沿って；N + に沿った + N
〜に沿って
〜に先立って Formal written "prior to," used when something is done in advance of a major event as a preliminary step. More restricted than 前に: the following event must be significant. — N + に先立って／に先立ち；V-dict + に先立って；N修飾は「に先立つ + N」
〜を通じて / 〜を通して Marks a medium or intermediary ("via, through"), or a period during the whole of which something holds. を通して leans slightly more toward active use of the means; both are fairly formal. — N（手段・媒介・期間）+ を通じて／を通して
〜に際して Formal written or ceremonial phrasing meaning "on the occasion of / when doing." Marks a special, one-off moment such as a signing, departure or opening, not a routine event. — N + に際して／に際し；V-dict + に際して；N修飾は「に際しての + N」
〜をはじめ Names the most representative member of a group first, implying many others follow. Formal written style, common in reports and announcements. — N + をはじめ／をはじめとして；N + をはじめとする + N
〜につれて "As … progresses," for two changes that advance gradually and in proportion. Neutral register, used in both speech and writing; not used for one-off events or intentional actions. — V-dict + につれて／につれ；N（変化を表す語）+ につれて
〜を問わず "Regardless of," saying that a difference in the named category makes no difference. Formal written style; typical in job ads, notices and rules. — N（年齢・経験・男女・昼夜 など）+ を問わず；「〜のいかんを問わず」も可
〜を中心に "Centering on / mainly," showing what stands at the core of an activity, spread or arrangement. Neutral-to-formal; common in news and business explanations. — N + を中心に／を中心として；N + を中心とする + N
〜に応じて "Depending on / in response to," where one thing varies flexibly as another varies. Formal; frequent in business and service language. — N（変化する物事・要望）+ に応じて／に応じ；N + に応じた + N
〜にわたって / 〜にわたる Formal expression for extent: something continues or spreads over a whole span of time, distance or range. The noun before it must express that span. にわたる modifies a noun. — N（期間・範囲）+ にわたって／にわたり；N + にわたる／にわたった + N